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  <front>
    <journal-meta>
      <journal-title-group>
        <journal-title>Scalable agent alignment via reward model-
ing: a research direction. arXiv:</journal-title>
      </journal-title-group>
    </journal-meta>
    <article-meta>
      <title-group>
        <article-title>Challenges for Using Impact Regularizers to Avoid Negative Side Effects</article-title>
      </title-group>
      <contrib-group>
        <contrib contrib-type="author">
          <string-name>David Lindner</string-name>
          <email>david.lindner@inf.ethz.ch</email>
          <xref ref-type="aff" rid="aff0">0</xref>
        </contrib>
        <contrib contrib-type="author">
          <string-name>Kyle Matoba</string-name>
          <email>kyle.matoba@ep</email>
          <xref ref-type="aff" rid="aff1">1</xref>
        </contrib>
        <contrib contrib-type="author">
          <string-name>Alexander Meulemans</string-name>
          <xref ref-type="aff" rid="aff2">2</xref>
        </contrib>
        <aff id="aff0">
          <label>0</label>
          <institution>Department of Computer Science</institution>
          ,
          <addr-line>ETH Zurich</addr-line>
        </aff>
        <aff id="aff1">
          <label>1</label>
          <institution>Idiap and EPFL</institution>
        </aff>
        <aff id="aff2">
          <label>2</label>
          <institution>Institute of Neuroinformatics, University of Zurich and ETH Zurich</institution>
        </aff>
      </contrib-group>
      <pub-date>
        <year>1811</year>
      </pub-date>
      <volume>07871</volume>
      <abstract>
        <p>Designing reward functions for reinforcement learning is difficult: besides specifying which behavior is rewarded for a task, the reward also has to discourage undesired outcomes. Misspecified reward functions can lead to unintended negative side effects, and overall unsafe behavior. To overcome this problem, recent work proposed to augment the specified reward function with an impact regularizer that discourages behavior that has a big impact on the environment. Although initial results with impact regularizers seem promising in mitigating some types of side effects, important challenges remain. In this paper, we examine the main current challenges of impact regularizers and relate them to fundamental design decisions. We discuss in detail which challenges recent approaches address and which remain unsolved. Finally, we explore promising directions to overcome the unsolved challenges in preventing negative side effects with impact regularizers.</p>
      </abstract>
    </article-meta>
  </front>
  <body>
    <sec id="sec-1">
      <title>1 Introduction</title>
      <p>
        Specifying a reward function in reinforcement learning (RL)
that completely aligns with the designer’s intent is a difficult
task. Besides specifying what is important to solve the task
at hand, the designer also needs to specify how the AI
system should behave in the environment in general, which is
hard to fully cover. For example, RL agents playing video
games often learn to achieve a high score without solving
the desired task by exploiting the game
        <xref ref-type="bibr" rid="ref25">(e.g. Saunders et al.
2018)</xref>
        . Side effects occur when the behavior of the AI system
diverges from the designer’s intent because of some
considerations that were not anticipated beforehand, such as the
possibility to exploit a game. In this work, we focus on side
effects that are tied to the reward function, which we define
as side effects that would still occur if we had access to an
oracle that finds an optimal policy for a given reward function.
We explicitly do not consider side effects resulting from the
used RL algorithm, which are often discussed using the term
safe exploration
        <xref ref-type="bibr" rid="ref7">(Garcıa and Ferna´ndez 2015)</xref>
        .
      </p>
      <p>In practice, the designer typically goes through several
iterations of reward specification to optimize the agent’s
performance and minimize side effects. This is often a tedious
*The authors contributed equally.</p>
      <p>Copyright ©2021 for this paper by its authors. Use permitted under
Creative Commons License Attribution 4.0 International (CC BY
4.0).
process and there is no guarantee that the agent will not
exhibit side effects when it encounters new situations. In fact,
such problems with misspecified reward functions have been
observed in various practical applications of RL (Krakovna
et al. 2020b).</p>
      <p>
        In most situations, it is useful to decompose the
reward R(s) into a task-related component Rtask(s) and an
environment-related component Renv(s), where the latter
specifies how the agent should behave in the environment,
regardless of the task.1 As
        <xref ref-type="bibr" rid="ref21">Shah et al. (2019)</xref>
        observe, Renv is
related to the frame problem in classical AI (McCarthy and
Hayes 1969): we not only have to make a prediction about
what is supposed to change, but also what is supposed to
remain unchanged. Renv is more prone to misspecification,
because it needs to specify everything that can happen beyond
a task, that can result in undesired outcomes. Because the
designer builds an RL agent to solve a specific problem, it
is relatively easy to anticipate considerations directly related
to solving the task in Rtask.
        <xref ref-type="bibr" rid="ref21">Shah et al. (2019)</xref>
        point out that
environments are generally already optimized for humans,
hence, defining Renv primarily requires to specify which
features of the environment the AI systems should not disturb.
Therefore, penalizing large changes in the current state of
the world can be thought of as a coarse approximation for
Renv.
      </p>
      <p>
        Impact regularization (IR) has emerged as a tractable and
effective way to approximate Renv
        <xref ref-type="bibr" rid="ref12 ref22 ref23 ref3">(Armstrong and
Levinstein 2017; Krakovna et al. 2019; Turner, Hadfield-Menell,
and Tadepalli 2020)</xref>
        . The main idea behind IR is to
approximate Renv through a measure of “impact on the
environment”, which avoids negative side effects and reduces the
burden on the reward designer.
      </p>
      <p>In this paper, we discuss IR of the form</p>
      <p>R(st) = Rspec(st)
d(st; b(s0; st 1; t))
(1)
where st denotes the state at time step t, Rspec denotes the
reward function specified by the designer,2 and:
• the baseline b(s0; st 1; t) provides a state obtained by
following a “default” or “safe” policy at timestep t and uses
1We write the reward function only as a function of states for
simplicity, as the state-space can be formally extended to include
the last action.</p>
      <p>2Rspec contains the specified parts of both Rtask and Renv.
either the initial state and the current time (s0; t) to
compute it, or else the current state st 1,
• d measures the deviation of the realized state from the
baseline state, and
•</p>
      <p>0 gives a global scale at which to trade off the
specified reward and the regularization.</p>
      <p>
        Composing these three terms gives a general formulation
of regularization that encompasses most proposals found in
the literature, but permits separate analysis
        <xref ref-type="bibr" rid="ref12">(Krakovna et al.
2019)</xref>
        .
      </p>
      <p>We start by giving an overview of the related work on
IR (Section 2), before we discuss the three main design
decisions for IR. First, we discuss how to choose a baseline
(Section 3), emphasizing considerations of environment
dynamics and a tendency for agents to offset their actions.
Second, we discuss how to quantify deviations from the
baseline (Section 4), especially the distinction between negative,
neutral, and positive side effects. Third, we discuss how to
choose the scale (Section 5). Finally, we propose some
directions to improve the effectiveness of IR (Section 6) .</p>
      <p>The main contribution of this work is to, discuss in
detail the current main challenges of IR, building upon
previous work, and to suggest possible ways forward to overcome
these challenges.</p>
      <p>2</p>
    </sec>
    <sec id="sec-2">
      <title>Related Work</title>
      <p>
        <xref ref-type="bibr" rid="ref1">Amodei et al. (2016)</xref>
        reviewed negative side effects as one
of several problems in AI safety, and discussed using
impact regularization (IR) to avoid negative side effects. Since
then, several concrete approaches to IR have been proposed,
of which eq. (1) gives the underlying structure.
        <xref ref-type="bibr" rid="ref3">Armstrong
and Levinstein (2017)</xref>
        proposed to measure the impact of the
agent compared to the inaction baseline, starting from the
initial state s0. The inaction baseline assumes the agent does
nothing, which can be formalized by assuming a non-action
exists.3
        <xref ref-type="bibr" rid="ref3">Armstrong and Levinstein (2017)</xref>
        emphasized the
importance of a semantically meaningful state
representation for the environment when measuring distances from the
inaction baseline. While
        <xref ref-type="bibr" rid="ref3">Armstrong and Levinstein (2017)</xref>
        discussed the problem of measuring the impact of an agent
abstractly,
        <xref ref-type="bibr" rid="ref12">Krakovna et al. (2019)</xref>
        proposed a concrete
deviation measure called Relative Reachability (RR). RR
measures the average reduction in the number of states reachable
from the current state, compared to a baseline state. This
captures the intuition that irreversible changes to the
environment should be penalized more, but has advantages over
directly using irreversibility as a measure of impact (as e.g.
in
        <xref ref-type="bibr" rid="ref6">Eysenbach et al. (2018)</xref>
        ), such as allowing to quantify the
magnitude of different irreversible changes.
      </p>
      <p>
        Turner, Hadfield-Menell, and Tadepalli (2020) and
        <xref ref-type="bibr" rid="ref12">Krakovna et al. (2019)</xref>
        generalized the concept of RR
towards Attainable Utility (AU) and Value Difference (VD)
3
        <xref ref-type="bibr" rid="ref3">Armstrong and Levinstein (2017)</xref>
        define this baseline as the
state the environment would be in when the agent would have never
been deployed. This is slightly different from the definition of the
inaction baseline we give here and that later work used, as the mere
presence of the agent can influence the environment.
measures respectively, which both share the same structural
form for the deviation measure:
      </p>
      <p>X
dVD(st; s0t) = X wxf Vx(s0t)
x=1</p>
      <p>
        Vx(st) ;
(2)
where x ranges over some sources of value, Vx(st) is the
value of state st according to x, wx is its weight in the sum
and f is a function characterizing the deviation between the
values. AU is a special case of this with wx = 1=X for all x
and the absolute value operator as f . This formulation
captures the same intuition as RR, but allows to measure the
impact of the agent in terms of different value functions,
instead of just counting states. Concretely, AU aims to
measure the agent’s ability to achieve high utility on a range of
different goals in the environment, and penalizes any change
that reduces this ability. Turner, Hadfield-Menell, and
Tadepalli (2020) also introduced the stepwise inaction baseline to
mitigate offsetting behavior (c.f. Section 3.2). This baseline
follows an inaction policy starting from the previous state
st 1 rather than the starting state s0. Follow-up work scaled
AU towards more complex environments
        <xref ref-type="bibr" rid="ref22 ref23">(Turner, Ratzlaff,
and Tadepalli 2020)</xref>
        .
      </p>
      <p>
        Krakovna et al. (2020a) built upon the VD measure and
introduced an auxiliary loss representing how well the agent
could solve future tasks in the same environment, given its
current state. This can be seen as a deviation measure in e.q.
(1) that rewards similarity with a baseline instead of
penalizing deviation from it.
        <xref ref-type="bibr" rid="ref6">Eysenbach et al. (2018)</xref>
        ’s approach
to penalize irreversibility can be seen as a special case of
Krakovna et al. (2020a).
      </p>
      <p>
        Aside from IR,
        <xref ref-type="bibr" rid="ref14">Rahaman et al. (2019)</xref>
        proposed to learn
an arrow of time, representing a directed measure of
reachability, using the intuition that irreversible actions tend to
leave the environment in a more disorderly state, making it
possible to define an arrow of time with methods inspired by
thermodynamics. As another alternative to IR, Zhang,
Durfee, and Singh (2018, 2020) proposed to learn which
environmental features an AI system is allowed to change by
querying a human overseer. They provided an active
querying approach that makes maximally informative queries.
        <xref ref-type="bibr" rid="ref21">Shah et al. (2019)</xref>
        developed a method for learning which
parts of the environment a human cares about by
assuming that the world is optimized to suit humans.
        <xref ref-type="bibr" rid="ref17 ref18">Saisubramanian, Kamar, and Zilberstein (2020</xref>
        ) formulated the side
effects problem as a multi-objective Markov Decision
Process, where they learn a separate reward function
penalizing negative side effects and optimize this secondary
objective while staying close to the optimal policy of the task
objective.
        <xref ref-type="bibr" rid="ref17 ref18">Saisubramanian, Zilberstein, and Kamar (2020</xref>
        )
provide a broad overview of the various existing approaches for
mitigating negative side effects, while we zoom in on one
class of approaches, IR, and discuss the corresponding
challenges in detail.
      </p>
      <p>3</p>
    </sec>
    <sec id="sec-3">
      <title>Choosing a Baseline</title>
      <p>Recent work mainly uses two types of baselines in impact
regularization (IR): (i) the inaction baseline b(s0; st; t) =
T (stjs0; inaction) and (ii) the stepwise inaction baseline
b(s0; st; t) = T (stjst 1; inaction), where T is the
distribution over states st when starting at state s0 or st 1
respectively and following the inaction policy inaction that always
takes an action anop that does nothing.</p>
      <p>
        Unfortunately, the inaction baseline can lead to
undesirable offsetting behavior, where the agent tries to undo the
outcomes of their task after collecting the reward, moving
back closer to the initial baseline
        <xref ref-type="bibr" rid="ref22 ref23">(Turner, Hadfield-Menell,
and Tadepalli 2020)</xref>
        . The stepwise inaction baseline
removes the offsetting incentive of the agent by branching off
from the previous state instead of the starting state
        <xref ref-type="bibr" rid="ref22 ref23">(Turner,
Hadfield-Menell, and Tadepalli 2020)</xref>
        . However, Krakovna
et al. (2020a) argued that offsetting behavior is desirable in
many cases. In section 3.2 we contribute to this discussion
by breaking down in detail when offsetting behavior is
desirable or undesirable, whereas in section 3.3, we argue that the
inaction baseline and step-wise inaction baseline can lead
to inaction incentives in nonlinear dynamical environments.
We start, however, with the fundamental observation that the
inaction baseline and stepwise inaction baseline do not
always represent safe policies in section 3.1.
3.1
      </p>
      <sec id="sec-3-1">
        <title>Inaction Baselines are not Always Safe</title>
        <p>The baseline used in IR should represent a safe policy where
the AI system does not harm its environment or itself. In
many cases, taking no actions would be a safe policy for the
agent, e.g. for a cleaning robot. However, if the AI system is
responsible for a task requiring continuous control, inaction
of the AI system can be disastrous. For example, if the agent
is responsible for driving a car on a highway, doing
nothing likely results in a crash. This is particularly problematic
for the stepwise inaction baseline, which follows an inaction
policy starting from the previous state. The inaction policy
starting from the initial state can also be unsafe, for example,
if an agent takes over the control of the car from a human,
and therefore the initial state s0 already has the car driving.</p>
        <p>For this reason, designing a safe baseline for a task or
environment that requires continuous control is a hard
problem. One possible approach is to design a policy that is
known to be safe based on expert knowledge. However, this
can be a time-consuming process, and is not always feasible.
Designing safe baselines for tasks and environments that
require continuous control is an open problem that has to be
solved before IR can be used in these applications.
3.2</p>
      </sec>
      <sec id="sec-3-2">
        <title>Offsetting</title>
        <p>An agent engages in offsetting behavior when it tries to undo
the outcomes of previous actions, i.e. when it “covers up its
tracks”. Offsetting behavior can be desirable or undesirable,
depending on which outcomes the agent counteracts.</p>
        <p>
          Undesirable offsetting. Using IRs with an inaction
baseline starting from the initial state can lead to undesirable
offsetting behavior where the agent counteracts the outcomes
of its task
          <xref ref-type="bibr" rid="ref12 ref22 ref23">(Krakovna et al. 2019; Turner, Hadfield-Menell,
and Tadepalli 2020)</xref>
          . For example,
          <xref ref-type="bibr" rid="ref12">Krakovna et al. (2019)</xref>
          consider a vase on a conveyor belt. The agent is rewarded
for taking the vase off the belt, hence preventing that it will
fall off the belt. The desired behavior is to take the vase and
stay put. The offsetting behavior is to take the vase off the
belt, collect the reward, and afterwards put the vase back on
the conveyor belt to reduce deviation from the baseline. To
understand this offsetting behavior recall the decomposition
of the true reward into a task-related and an
environmentrelated component from section 1. A designer usually
specifies a task reward Rstapsekc that rewards states signaling task
completion (e.g. taking the vase off the belt). However, each
task has consequences to the environment, which often are
the reason why the task should be completed in the first place
(e.g. the vase being not broken). In all but simple tasks,
assigning a reward to every task consequence is impossible,
and so by omission, they have a zero reward. When IR
penalizes consequences of completing the task, because they
differ from the baseline, this results in undesirable
offsetting behavior. The stepwise inaction baseline
          <xref ref-type="bibr" rid="ref22 ref23">(Turner,
Ratzlaff, and Tadepalli 2020)</xref>
          successfully removes all offsetting
incentives. However, in other situations offsetting might be
desired.
        </p>
        <p>Desirable Offsetting. In many cases, offsetting behavior
is desired, because it can prevent unnecessary side effects.
Krakovna et al. (2020a) provide an example of an agent
which is asked to go shopping, and needs to open the front
door of the house to go to the shop. If the agent leaves the
door open, wind from outside can knock over a vase
inside, which the agent can prevent by closing the door after
leaving the house. When using the stepwise inaction
baseline (with rollouts, c.f. Section 4.2), the agent gets
penalized once when opening the door for knocking over the vase
in the future, independent of whether it closes the door
afterwards (and thus prevents the vase from breaking) or not.
Hence, for this example, the offsetting behavior (closing the
door) is desirable. The reasoning behind this example can be
generalized to all cases where the offsetting behavior
concerns states that are instrumental towards achieving the task
(e.g. opening the door) and not a consequence of completing
the task (e.g. the vase being not broken).</p>
        <p>A Crucial Need for a New Baseline. The recently
proposed baselines either remove offsetting incentives
altogether or allow for both undesirable and desirable offsetting
to occur, which are both unsatisfactory solutions. Krakovna
et al. (2020a) proposed resolving this issue by allowing all
offsetting (e.g. by using the inaction baseline) and rewarding
all states where the task is completed in the specified reward
function. However, we attribute three important downsides
to this approach. First, states that occur after task
completion can still have negative side effects. If the reward
associated with these states is high enough to prevent offsetting,
it might also be high enough to encourage the agent to
pursue these states and ignore their negative side effects.
Second, not all tasks have a distinct goal state that indicates the
completion of a task, but rather accumulate task-related
rewards at various time steps during an episode. Third, this
approach creates a new incentive for the agent to prevent
shut-down, as it continues to get rewards after the task is
completed (Hadfield-Menell et al. 2017).</p>
        <p>We conclude that offsetting is still an unsolved problem,
highlighting the need for a new baseline, to prevent
undesirable offsetting behavior, but allow for desirable offsetting.
In dynamic environments that are highly sensitive to the
agent’s actions, the agent will be susceptible to inaction
incentives. Either the agent does not act at all (for all but small
magnitudes of ) or it will be insufficiently regularized and
possibly result in undesired side effects (for small ).</p>
        <p>
          Sensitivity to Typical Actions. Many real-world
environments exhibit chaotic behavior, in which the state of the
environment is highly sensitive to small perturbations. In such
environments, the environment state where the agent has
performed an action will be fundamentally different from
the environment state for the inaction baseline
          <xref ref-type="bibr" rid="ref3">(Armstrong
and Levinstein 2017)</xref>
          . Furthermore, for the step-wise
inaction baseline, the same argument holds for the non-action
compared to the planned action of the agent. Hence, when
using these baselines for IR, all actions of the agent will be
strongly regularized, creating the inaction incentive. When
is lowered to allow the agent to take actions, the agent can
cause negative side effects when the IR cannot differentiate
between negative side effects and chaotic changes in the
environment. Here, it is useful to distinguish between typical
and atypical actions. We say (informally) that an action is
typical if it is commonly used for solving a wide variety of
tasks (e.g. moving). When the environment is highly
sensitive to typical actions, IRs with the current baselines will
prevent the agent from engaging in normal operations.
However, it is not always a problem if the environment is highly
sensitive to atypical actions of the agent (e.g. discharging
onboard weaponry), as preventing atypical actions impedes
less with the normal operation of the agent.
        </p>
        <p>Capability of the Agent. The inaction incentive will
become more apparent for agents that are highly capable of
predicting the detailed consequences of their actions, for
example by using a powerful physics engine. As the ability to
predict the consequences of an action is fundamental to
minimizing side effects, limiting the prediction capabilities of an
agent to prevent the inaction incentive is not desired. Rather,
for agents that can very accurately predict the implications
of their actions, it is necessary to have an accompanying
intelligent impact regularizer.</p>
        <p>
          State Features.
          <xref ref-type="bibr" rid="ref3">Armstrong and Levinstein (2017)</xref>
          point
out that for IR one should not represent states with overly
fine-grained features, as presenting an agent with too much
information exposes them to basing decisions on
irrelevancies. For example, it would be counterproductive for an
agent attempting to forecast demand in an online sales
situation to model each potential customer separately, when
broader aggregates would suffice. However, there remain
two issues with this approach to mitigate the inaction
incentive. First, the intrinsic dynamics of the environment
remain unchanged, so it is still highly sensitive to small
perturbations, of which the results can be visible in the coarser
features (e.g. the specific weather conditions). Second, for
advanced AI systems, it might be beneficial to change their
feature representation to become more capable of predicting
the consequences of their actions. In this case, one would
have no control over the granularity of the features.
        </p>
        <p>Deviation Measures. At the core of the inaction
problem is that some negative side effects are worse than others.
Usually, it does not matter if the agent changes the weather
conditions by moving around, however, it would matter if
the agent causes a serious negative side effect, for example
a hurricane. While both outcomes can be a result of
complex and chaotic dynamics of the environment, we care less
about the former and more about the latter. Differentiating
between negative, neutral and positive side effects is a task
of the deviation measure used in the IR, which is discussed
in the next section.</p>
        <p>4</p>
      </sec>
    </sec>
    <sec id="sec-4">
      <title>Choosing a Deviation Measure</title>
      <p>
        A baseline defines a “safe” counterfactual to the agent’s
actions. The deviation measure determines how much a
deviation from this baseline by the agent should be
penalized or rewarded. Currently, the main approaches to a
deviation measure are the relative reachability (RR) measure
        <xref ref-type="bibr" rid="ref12">(Krakovna et al. 2019)</xref>
        , the attainable utility (AU) measure
        <xref ref-type="bibr" rid="ref22 ref23">(Turner, Hadfield-Menell, and Tadepalli 2020)</xref>
        and the
future task (FT) reward
        <xref ref-type="bibr" rid="ref22 ref23">(Krakovna et al. 2020a)</xref>
        . In the
practical implementations of AU and FT, they use reachability
tasks, which can be considered as a sub-sampling of RR. In
this section, we argue that the current deviation measures
should be augmented with a notion of value of the impact to
avoid unsatisfactory performance of the agent and that new
rollout policies should be designed that allow for a proper
incorporation of delayed effects into the deviation measure.
4.1
      </p>
      <sec id="sec-4-1">
        <title>Which Side Effects are Negative?</title>
        <p>
          The goal of IRs is to approximate Renv for all states in a
tractable manner. It does this by penalizing impact on the
environment, built upon the assumption that the environment is
already optimized for human preferences
          <xref ref-type="bibr" rid="ref21">(Shah et al. 2019)</xref>
          .
The IR aims to penalize impact proportionally to the
magnitude of this impact which corresponds with the magnitude
of the side effect
          <xref ref-type="bibr" rid="ref12 ref22 ref23">(Krakovna et al. 2019; Turner,
HadfieldMenell, and Tadepalli 2020)</xref>
          . However, not all impact is
negative, but it can also be neutral or even positive. Renv does not
only consider the magnitude the impact on the environment,
but also to which degree this impact is negative, neutral or
positive. Neglecting the associated value of impact can lead
to suboptimal agent behavior, as highlighted in the example
below.
        </p>
        <p>Example: The Chemical Production Plant. Consider
an AI system controlling a plant producing a chemical
product for which various unknown reactions exist, each
producing a different combination of waste products. The task of
the AI system is to optimize the production rate of the plant,
i.e. it gets a reward proportional to the production rate. To
minimize the impact of the plant on the environment, the
reward function of the agent is augmented with an impact
regularizer, which penalizes the mass of waste products
released in the environment, compared to an inaction baseline
(where the plant is not operational). Some waste products
are harmless (e.g. O2), whereas others can be toxic. When
the deviation measure of the impact regularizer does not
differentiate between negative, neutral or positive impact,
the AI system is incentivized to use a reaction mechanism
that maximizes production while minimizing waste.
However, this reaction might output mostly toxic waste product,
whereas another reaction outputs only harmless waste
products and hence has no negative side effects. Tuning the
regularizer magnitude does not provide a satisfactory solution
in this case, as either the plant is not operational (for high
lambda), or the plant is at risk of releasing toxic waste
products in the environment.</p>
        <p>Positive Side Effects. The distinction between positive,
neutral and negative impact is not only needed to allow for
a satisfactory performance of the agent in many
environments, it is also desirable for encouraging unanticipated
positive side effects. Expanding upon the example in 4.1: if the
agent discovered a way to costlessly sequester carbon
dioxide alongside its other tasks it should do so, whilst an IR
would encourage the robot to not interfere. While very
positive unexpected outcomes might be unlikely, this possibility
should not be neglected in the analysis of impact
regularizers.</p>
        <p>
          Value Differences. To distinguish between positive,
neutral and negative side effects, we need an approximation of
Renv that goes beyond measuring impact as a sole source
of information. The value difference framework
          <xref ref-type="bibr" rid="ref22 ref23">(Turner,
Hadfield-Menell, and Tadepalli 2020)</xref>
          allows for
differentiating between positive and negative impact by defining the
deviation measure as a sum of differences in value between
a baseline and the agent’s state-action pair for various value
functions. Hence, it is possible to reflect how much the
designer’s values different kinds of side effects in these value
functions. However, the challenge remains to design value
functions that approximate Renv to a sufficient degree on the
complete state space, which is again prone to reward
misspecification. So although the value difference framework
allows for specifying values for side effects, how to specify
this notion of value is still an open problem.
4.2
        </p>
      </sec>
      <sec id="sec-4-2">
        <title>Rollout Policies</title>
        <p>
          Often, the actions of an agent cause delayed effects, i.e.
effects that are not visible immediately after taking the action.
The stepwise inaction baseline
          <xref ref-type="bibr" rid="ref22 ref23">(Turner, Hadfield-Menell,
and Tadepalli 2020)</xref>
          ignores all actions that took place
before t 1, hence, to correctly penalize delayed effects, the
deviation measure needs to incorporate future effects. This
can be done by collecting rollouts of future trajectories
using a simulator or model of the environment. These rollouts
depend on which rollout policy is followed by the agent in
the simulation. For the baseline states, the inaction policy
is the logical choice. For the rollout of the future effects of
the agent’s action, it is less clear which rollout policy should
be used. Turner, Hadfield-Menell, and Tadepalli (2020) use
the inaction policy in this case. Hence, this IR considers a
rollout where the agent takes its current action, after which
it cannot do any further actions. This approach has
significant downsides, because IR does not allow the agent to do a
series of actions when determining the impact penalty (e.g.
the agent can take an action to jump, but cannot plan for its
landing accordingly in the rollout). Therefore, we argue that
future work should develop rollout policies different from
the inaction policy, such as the current policy of the agent.
5
        </p>
      </sec>
    </sec>
    <sec id="sec-5">
      <title>Choosing the Magnitude of the Regularizer</title>
      <p>To combine the IR with a specified reward function, the
designer has to choose the magnitude of the regularizer
. Turner, Hadfield-Menell, and Tadepalli (2020) say that
“loosely speaking, can be interpreted as expressing the
designer’s beliefs about the extent to which R [the specified
reward] might be misspecified”.</p>
      <p>
        It is crucial to choose the correct . If is too small, the
regularizer may not reduce the risk of undesirable side
effects effectively. If is too big, the regularizer will overly
restrict necessary effects of the agent on the environment,
and the agent will be less effective at achieving its goal.
Note, that while the regularizers proposed by
        <xref ref-type="bibr" rid="ref12">Krakovna et al.
(2019)</xref>
        and Turner, Hadfield-Menell, and Tadepalli (2020)
already measure utility, in general must also handle a
unitconversion of the regularizer to make it comparable with the
reward function.
      </p>
      <p>
        Some intuition for choosing comes from a Bayesian
perspective, where the regularizer encodes prior knowledge and
controls how far from the prior the posterior should have
moved. Another distinct view on setting comes from the
dual optimization problem, where it represents the Lagrange
multiplier on an implied set of constraints: is the
magnitude of the regularizer for which the solution to the
penalized optimization problem coincides with a constrained
optimization problem. Hence, the designer can use to
communicate constraints to the AI system, which is a natural way
to phrase some common safety problems
        <xref ref-type="bibr" rid="ref15">(Ray, Achiam, and
Amodei 2019)</xref>
        .
      </p>
      <p>
        <xref ref-type="bibr" rid="ref3">Armstrong and Levinstein (2017)</xref>
        discuss the problem of
tuning and note that contrary to intuition the region of
useful ’s can be very small and hard to find safely. In practice
is often tuned until the desired behavior is achieved, e.g., by
starting with a high and reducing it until the agent achieves
the desired behavior. This approach is in general insufficient
to find the correct trade-off. For a fixed step-size in
decreasing , the tuning might always jump from a that leads to
inaction, to a that yields unsafe behavior. The same holds
for other common procedures to tune hyperparameters.
6
      </p>
    </sec>
    <sec id="sec-6">
      <title>Ways Forward</title>
      <p>In this section, we put forward promising future research
directions to overcome the challenges discussed in the
previous sections.
6.1</p>
      <sec id="sec-6-1">
        <title>A Causal Framing of Offsetting</title>
        <p>In Section 3.2, we highlighted that some offsetting behavior
is desired and some undesired. To design an IR that allows
for desired offsetting but prevents undesired offsetting, one
firsts needs to have a mechanism that can predict and
differentiate between these two types of offsetting. Undesired
offsetting concerns the environment states that are a
consequence of the task. The difficulty lies in determining which
states are a causal consequence of the task being completed
and differentiate them from states that could have occurred
regardless of the task.</p>
        <p>
          Goal-based Tasks. When the task consists of reaching a
certain goal state, the consequences of performing a task can
be formalized in a causal framework
          <xref ref-type="bibr" rid="ref13">(Pearl 2009)</xref>
          . When a
causal graph of the environment-agent-interaction is
available, the states that are a consequence of the task can be
obtained from the graph as the causal children nodes of the
goal state. Hence, a baseline that allows for desired
offsetting behavior but prevents undesired offsetting behavior
prevents the agent from interfering with the children nodes of
the goal states, while allowing for offsetting on other states.
        </p>
        <p>
          General Tasks. Not all tasks have a distinct goal state
which indicates the completion of a task, but accumulate
instead task-related rewards at various time steps during an
episode. Extending this argument to general tasks remains
an open issue, for which causal influence diagrams
          <xref ref-type="bibr" rid="ref5">(Everitt
et al. 2019)</xref>
          can provide a mathematical framework.
6.2
        </p>
      </sec>
      <sec id="sec-6-2">
        <title>Probabilities Instead of Counterfactuals as</title>
      </sec>
      <sec id="sec-6-3">
        <title>Baseline</title>
        <p>
          <xref ref-type="bibr" rid="ref3">Armstrong and Levinstein (2017)</xref>
          made the interesting
argument that probabilities are better suited than counterfactuals
for measuring the impact of actions. Current
implementations of IRs use a counterfactual as baseline (e.g. the inaction
baseline or stepwise inaction baseline). Because this
baseline is one specific trajectory, it will differ considerably from
the actual trajectory of the agent in environments that
exhibit chaotic dynamics. However, chaotic environments will
also be highly sensitive to perturbations that do not
originate from the agent’s actions. One possible way forward
towards a more robust measure of the agent’s impact on the
environment is hence to compare probabilities that
marginalize over all external perturbations instead of comparing
specific trajectories. Define p(stjA) as the probability of having
state st, given the trajectory of actions A the agent took and
p(stjB) as the probability of st given actions prescribed by
the baseline. All influences of perturbations that did not arise
from the agent are marginalized out in these probabilities.
Hence, a divergence measure between these two
probabilities can give a more robust measure of potential impact of
the agent, without being susceptible to non-necessary
inaction incentives. To our best knowledge, this idea has not yet
been implemented as a concrete IR method and would hence
be a promising direction for future research.
6.3
        </p>
      </sec>
      <sec id="sec-6-4">
        <title>Improved Human-Computer interaction</title>
        <p>
          Side effects occur if there is a difference between the
outcome an AI system achieves and the intent of its (human)
designer. Thus improving how well the designer can
communicate their intent to the AI system is an important aspect
of eliminating side effects (Leike et al. 2018). This
emphasis on the human component of learning to avoid negative
side effects connects it closely to the problem of scalable
oversight proposed by
          <xref ref-type="bibr" rid="ref1">Amodei et al. (2016)</xref>
          .
        </p>
        <p>
          Improved Tools for Reward Designers. Commonly, a
designer will aim to iteratively improve the AI system and
its reward function. Similarly, when choosing an impact
regularizer, a designer will iterate on the choice of baseline,
deviation measure, and regularization strength and test them
in a sequence of environments that increasingly resemble
the production environment. At each iteration, the designer
identifies weaknesses and corrects them, such that the
criterion being optimized becomes increasingly true to the
designer’s intent. For example, an AI with the goal to trade
financial assets may be run against historical data
(“backtested”) in order to understand how it might have reacted
in the past, and presented with deliberately extreme inputs
(“stress-tested”) in order to understand likely behavior in
“out of sample” situations. To design a reward function and
a regularizer, it is crucial for the designer to be able to
understand how the system would react in novel situations and
how to fix it in case it exhibits undesired behavior. Further
research aiming to increase the designer’s ability to
understand how a system will react, will substantially help the
designer to communicate their intent more effectively. Recent
work in this direction concerning interpretability
          <xref ref-type="bibr" rid="ref8">(Gilpin
et al. 2018)</xref>
          , verification
          <xref ref-type="bibr" rid="ref10">(e.g. Huang et al. 2017)</xref>
          of machine
learning models is particularly promising.
        </p>
        <p>
          Actively Learning from Humans. Considering the
problem from the perspective of the AI system, the goal is to
improve its ability to understand the designer’s intent,
especially in novel, unanticipated, scenarios. Instead of the
designer telling the system their intent, this problem can be
addressed by the system asking the designer about their
intent. To decide what to ask the designer, the system may be
able to determine which states it is highly uncertain about,
even if it is not able to accurately ascribe values to some
of them. Recent work shows that such an approach can be
effectively used to learn from the human about a task at
hand
          <xref ref-type="bibr" rid="ref4">(Christiano et al. 2017)</xref>
          , but it may also be used to
learn something about the constraints of the environment
and which side effects are desired or undesired
          <xref ref-type="bibr" rid="ref25">(Zhang,
Durfee, and Singh 2018)</xref>
          . Active learning could also provide a
different perspective on impact regularizers: instead of
directly penalizing impact on the environment, a high value
of the regularization term could be understood as indicating
that the designer should give feedback. In particular, this
approach could help to resolve situations in which a positive
task reward conflicts with the regularization term.
7
        </p>
      </sec>
    </sec>
    <sec id="sec-7">
      <title>Conclusion</title>
      <p>Avoiding negative side effects in systems that have the
capacity to cause harm is necessary to fully realize the promise
of artificial intelligence. In this paper, we discussed a
popular approach to reduce negative side effects in RL: impact
regularization (IR). We discussed the practical difficulty of
choosing each of the three components: a baseline, a
deviation measure and a regularization strength. Furthermore, we
pointed to fundamental problems that are currently not
addressed by state-of-the-art methods, and presented several
new future research directions to address these. While our
discussion showed that current approaches still leave
significant opportunities for future work, IRs are a promising idea
for building the next generation of safe AI systems, and we
hope that our discussion is valuable for researchers trying to
build new IRs.</p>
    </sec>
    <sec id="sec-8">
      <title>Acknowledgments</title>
      <p>We thank Andreas Krause, Franc¸ois Fleuret and Benjamin
Grewe for their valuable comments and suggestions. Kyle
Matoba was supported by the Swiss National Science
Foundation under grant number FNS-188758 “CORTI”.</p>
      <p>Krakovna, V.; Orseau, L.; Ngo, R.; Martic, M.; and Legg, S.
2020a. Avoiding Side Effects By Considering Future Tasks.
In Advances in Neural Information Processing Systems.</p>
      <p>McCarthy, J.; and Hayes, P. 1969. Some philosophical
problems from the standpoint of ai, Machine Intelligence
(Meltzer B. and Michie D., eds.), vol. 4.</p>
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