Anticipatory thinking is a complex cognitive process for assessing and managing risk in many contexts. Humans use anticipatory thinking to identify potential future issues and proactively take actions to manage their risks. In this paper we define a cognitive systems approach to anticipatory thinking as a metacognitive goal reasoning mechanism. The contributions of this paper include (1) defining anticipatory thinking in the MIDCA cognitive architecture, (2) operationalizing anticipatory thinking as a three step process for managing risk in plans, and (3) a numeric risk assessment calculating an expected cost-benefit ratio for modifying a plan with anticipatory actions.
Anticipatory Thinking (AT) is the deliberate and divergent
analysis of relevant future states that is a critical skill in
medical, military, and intelligence analysis
However, AI systems have yet to adopt this capability.
While agents with a metacognitive architecture can
formulate their own goals or adapt their plans in response to
their environment
To address this limitation, we take a step towards imagination machines with a contribution that operationalizes the concept of anticipatory thinking, a cognitive process reliant on an ample supply of imagination, as a metacognitive capability. We propose this capability as a kind of solution formulation method, a post-planning step that analyzes a solution plan for potential weaknesses and modifies the solution plan to account for them. This approach is in contrast to problem formulation, a pre-planning step that analyzes a problem for efficient search strategies, as well as online riskaware planning processes (Huang et al. 2019). Our first step of AT identifies properties of a plan that are prone to failure. These include concepts such as atoms needed throughout a plan but are only achieved in the initial state. As a second step, we extend goal-reasoning agent expectations to include anticipatory expectations, a kind of expectation derived from a plan’s relevant states that identifies exogenous sources that could potentially introduce failures. Finally, we define anticipatory reasoning to proactively mitigate the potential failures. An agent reasons over the conditions in the anticipatory expectations, generating anticipatory actions to be executed at specific times, foiling an exogenous source of failure. To exercise this new capability we use a simple example and define metrics for evaluating an agent’s anticipatory thinking.
Our contributions are based on three related areas of work. Prospective cognition is a fledgling field in cognitive psychology the goal of which is to understand human ability to reason about and imagine the future. We discuss some prospection modalities. The second area, goal-reasoning agents, is a type of agent that adapts to and formulates their own goals in response to their environment. We highlight some of the overlap between prospection modalities and the agent’s methods for formulating and achieving goals. Finally, investigations into metacognition’s role in decision making and behavior draws a close tie with autonomy. We detail some of the existing capability to frame anticipatory thinking’s role.
Anticipatory thinking is an emerging concept in
psychology
Divergent thinking is often used to assess individual
differences in creativity and has been part of scientific studies
on creativity since the 1960’s
Lastly, the emerging field of prospection is the ability
to reason about what may happen in the future.
One approach to mitigate risks is to encode mappings from states to goals, such that when an agent is in a state, it should pursue the corresponding goal. Thus, if risks are known at design time, an agent can be given mappings from risky states to mitigating goals. MADBot (Coddington et al. 2005) investigated goal formulation via motivator strategies within, and external to, the planning process. An example of a motivator function is the following: a rover robot may have the motivator function that when its battery level drops below a threshold, the agent will generate a goal to have a fully charged battery. This would then be achieved by a plan for the rover to navigate to the power source and plug itself in. As shown in Coddington (2005) these motivator functions can be either (1) encoded into the plan operators as constraints (i.e. every action has a precondition that the battery level is above a threshold) or (2) a separate goal formulation process which runs outside the planner and generates a new goal when motivator functions trigger.
Other approaches to mitigating risk with planning systems
include rationale-based monitors
Metacognition refers to processes that reason about
cognition in some form or another
At a general level it seems that AT could be considered a cognitive process since the objective of AT is to prevent risk that arises from various world states in order to achieve some goal that is a world state. When considering specific AT processes (presented in the next section) we argue that AT is truly a metacognitive process since it is concerned with meta goals such as achieved(g’) where g’ is a cognitive level goal. AT is also concerned with decision making on resource trade-offs (a type of metareasoning) for risk mitigation (i.e. spending X extra actions to mitigate Y potential risks). Additionally, if AT processes were to take into account an agent’s likelihood of succeeding at a task, than AT processes are making use metacognition self-prediction mechanisms.
MIDCA is currently under active development, and
until recently most work has consisted of implementation at
the cognitive level. Prior work on the metacognitive level
includes monitoring capabilities that maintain a cognitive
trace and control actions capable of switching planning
algorithms at runtime
Our approach to operationalizing anticipatory thinking
begins with the concept as explained in
First, in Section 3.1 we identify goal vulnerabilities as an example method in the deliberation step. This step reasons over a plan’s structure to identify properties that would be particularly costly were they not to go according to plan. A second step, failure anticipation, identifies sources of failure for the vulnerabilities in Section 3.2. Sources of failure can range from unknown environment states to other agent’s interfering goals. Finally, in Section 3.3 we detail a failure mitigation step that modifies an existing plan, reducing the exposure to the sources of failure and creating an anticipatory expectation. We capture these steps as a process in Table 1 1It is worth noting that while expectations at the cognitive and metacognitive levels have analogous roles, their definitions at each level are different.
2The Interpret phase generally includes discrepancy detection,
explanation/diagnosis, and goal formulation. Of these, discrepancy
detection is the only one with prior work at the metacognitive layer
of MIDCA.
and demonstrate these steps through an NBeacons running
example from
To illustrate these ideas, it is useful to consider following example. An agent must generate plans to reach beacons and activate them. If the agent ever passes through a sandpit square, they must take three actions to dig out. The wind may blow in a known direction at a known speed after every agent action. The wind pushes an agent a number of squares further (equivalent to the speed) in the wind’s direction and can result in an agent passing over a sandpit and getting stuck. In our example, the wind is blowing West at a speed of five making an agent’s plan vulnerable to any sandpit that lies within five squares West of their location.
We use the Partial Order Causal Link (POCL)
representation
Definition 1 (Causal link threat) A causal link threat ocp curs when a causal link s ! u between steps s and u for literal p, and some other step w has effect :p and could be executed after s but before u. Executing w in this interval establishes :p making the precondition p of u no longer satisfied by the effect p of s and thus u will not execute.
Identifying a plan’s vulnerable structural properties is the first step in proactively mitigating its failure. We define a single vulnerability, precondition strength, of what could be numerous vulnerable properties of a plan. Precondition strength, is a measure of how many times a precondition is established and used in plan. The fewer times a precondition is established and the more it is used increases the vulnerability of a plan to failure. It is useful in AT to identify literals that have a weak precondition strength, as their failure can require many repairs to a plan or eliminating an area of the solution space entirely.
strength of a plan , PRESTRENGTH( ), is a set of tuples ha; k; ei where a is a literal, k is the number of steps in that use a as a precondition, and e the number of times a is an effect before it is first used as precondition.
Our example in Figure 3, A is the agent’s location, ˜ are the sandpits, and 1 is the beacon location, and the optimal path from the agent’s location to the beacon is in orange. The optimal path comprises of eight move actions all of which have the (canMove) precondition. This precondition is only established once in the initial state and so its entry in PRESTRENGTH( ) is hcanM ove(agent); 8; 1i.
Vulnerabilities are not by themselves indicative that a plan is at risk of failure. Risk of failure requires some means to exploit the vulnerability, what we will call conditioning events. We approach identifying these events as a kind of prefactual reasoning (future-oriented counterfactual reasoning), where we take the negation of the most vulnerable preconditions (identified in Section ) and identify actions with them as effects.
events CE( ) of a plan are actions in the domain model such that one or more effects of each action is the negation of a precondition of a step in , introducing a causal link threat.
In our NBeacons example, wind may blow after each agent action and gives rise to a conditioning event. If the wind blows at any point where a sandpit is within five squares West of the agent, a causal link threat is introduced by the effect :canMove(agent). This results in four potential conditioning events, one after each of the agent’s first four moves, indicated by the red CE notation in Figure 3. After finding themselves in a sandpit, an agent must spend three actions digging out of the sand pit in order make canMove(agent) true and be able move again. We term these three dig actions as the impact of a conditioning event. Definition 4 (Impact) The impact of a conditioning event, impact(CE), is the cost of the actions needed to remove the causal link threat introduced by the conditioning event.
The final step to operationalizing anticipatory thinking is to define what the relevant property means for a goal-reasoning agent. We term this step failure mitigation where the agent reasons over conditioning events to identify actions that reduce a plan’s risk exposure to these conditioning events. These actions are anticipatory actions.
tions ANT( ) of a plan is a set of tuples hAANT; CEi where AANT is an action sequence, ai; a2; :::an added to such that at least one effect reduces the impact of the conditioning events CE in CE( ).
To mitigate the unpleasantness of being blown about by the wind and getting trapped in a sandpit, our agent has the option to outfit itself with a grappling hook. A grappling hook allows an agent to move out of a sandpit in a single action. However, adding the grappling hook adds action costs of one for the buy and pack steps that need to be executed. We add these two anticipatory actions to the agent’s plan before the journey begins, see 0 in Figure 4.
Adding the grappling hook to the plan creates an expectation within an agent that risk exposure to the wind conditioning event has been reduced. We refer to this new type of expectation as an anticipatory expectation and define it as:
tory Expectation is the action cost reductions expected from introducing anticipatory actions to mitigate conditioning events.
We now put forth an anticipatory thinking approach as a metacognitive process in MIDCA, highlighting the role of each phase of the metacognitive layer: Monitor: Obtain observations of the cognitive level components, including the current plan and the current goal g.
Discrepancy Detection: Flag the current plan from the cognitive level Plan phase (see Figure 1, cognitive layer, left side) as potentially risky, risk level( , HIGH).
Explanation / Diagnosis: Assess the risks associated with the plan using anticipatory thinking approaches, such as those described in Section using the notions of prestrength. The results of the analysis would be vulnerabilities V of the plan .
Goal Formulation: Formulate the goal to transform into a new plan 0 with a safer risk level, while maintaining that the current goal of is achieved. The new goal would then be frisk level( 0, LOW) ^ achieves( 0; g)g.
Evaluate: Drop any meta goals if they have been achieved. Intend: Commit to achieving the newly formulated meta goal frisk level( 0, LOW) ^ achieves( 0; g)g.
Plan: Take current mental state containing risk level( ,HIGH) and vulnerabilities V and search for a set of new actions, meta plan mp, consisting of add or delete edits from plan in order to achieve 0 such that frisk level( 0, LOW) ^ achieves( 0; g)g.
Control: Carry out the sequence of plan edits in mp resulting in a new 0 such that risk level( 0,LOW) and 0 j= g where g is the original goal of .
The primary effort occurs in the Plan phase which we speculate could be modeled as a search process such that nodes are plans and their associated risk levels and edges between nodes are anticipatory actions that are added to (or possibly removed from) the plan. The search process would terminate when a goal node is reached that meets a low risk level for the plan inside the node. This example through the metacognitive phases serves as one possible realization of AT in MIDCA. We leave more concrete implementation details for future work. Anticipatory thinking is concerned with identifying possible worlds that affect desirable outcomes and taking action to mitigate them. This differs from typical future-oriented analysis centered around prediction that is focused on identifying a single likely outcome. As such, to appropriately evaluate anticipatory thinking we require alternative measures than those used in prediction.
Conceptually, anticipatory thinking’s goal is to have a high recall rate. More specifically, it is to ensure that the events that ultimately occur are accounted for in a set of possible futures. However, calculating recall does not capture the cost of adding anticipatory actions or the cost of identifying conditioning events. To address this limitation we develop an assessment of anticipatory thinking that accounts for the cost in relation to the potential benefits.
An additional challenge is to avoid coupling anticipated outcomes to the actual outcomes. AT mitigates, rather than predicts, failure. Therefore AT assessment should only assess the potential payoff from mitigating, not whether any individual future comes to pass.
In Figure 5, we represent anticipatory thinking as a plan’s identified conditioning events in the green circle. Before anticipatory thinking, conditioning events are unknown to our agent and reside in the blue area. Successful anticipatory thinking is the set of identified conditioning events where anticipatory actions are taken to mitigate their impact and reside in the yellow area. We assess successful anticipatory thinking as AT assess( ) = jCE(AN T )j jCEj 0 impact(CEj ) 1
C ! CCC ;
A (1) where jCEj is the number of conditioning events identified and jCE(AN T )j are the mitigated conditioning events. Their ratio represents how many conditioning events were mitigated. A second ratio calculates the potential benefit of mitigation. In the numerator, we calculate the cost of all anticipatory actions with AANT(ANT) where we assume an action cost to one. For each anticipatory action set, ANT, we sum the impact of each mitigated conditioning event mitigated, impact(CEj ).
Applying equation 1 to our NBeacons conditioning events, we have four wind conditioning events, jCEj = 4, and each one is mitigated, jCE(AN T )j = 4. This ratio of 1.0 (4=4) is best possible case in that every identified conditioning event was mitigated. Conversely, plans where many identified conditioning events that have few mitigations would have a ratio closer to zero and may benefit from the use of robust search algorithms. Our next ratio assesses the potential mitigation benefit. Mitigating the wind event requires buying and packing the grappling hook, each with an action cost of one for a total of two, jAA(ANTi)j = 2. The sole anticipatory action sequence, i = 1, is expected to save the agent three dig actions for each of the four wind events, j = 4, resulting in a potential mitigation of twelve actions, and a resulting mitigation ratio of 0.83 (1 0:17). Again, plans with not so favorable benefits from mitigations would have a lower expected payoff from their actions and would have a ratio closer to zero. Together these two ratios result in an AT assess( 0) of 0.83 (1:0 0:83), this calculation is reflected in Equation 2.
AT assess( 0) = 4 4 0 P1 (3 + 3 + 3 + 3) ACC ; (2) i
Anticipatory thinking is a complex cognitive process for assessing and managing risk in many contexts. It allows humans to identify potential future issues and proactively take actions in the present that will manage their risks. We have defined how an artificial agent may perform anticipatory thinking at a goal reasoning level, so they may receive the same benefits and enable further autonomous capability.
Our approach made three contributions. First we defined anticipatory thinking in the MIDCA cognitive architecture as a goal reasoning process at the metacognitive layer. Specifically, Section highlights the role of AT in each phase of the metacognitive layer of MIDCA shown in Figure 2. Second, we operationalized the anticipatory thinking concept as a three step process for managing risk in plans. Goal vulnerabilities, failure anticipations and failure mitigation identify weakness of a plan, their potential failure sources (conditioning events), and failure mitigations (anticipatory actions) to reduce the impact of the failure sources. Finally, we proposed a numeric assessment for successful anticipatory thinking. Key to the assessment are a ratio of identified conditioning events to mitigated ones and an expected costbenefit ratio for the anticipatory actions.
We expect two immediate areas of future work. First, we are planning to integrate our anticipatory thinking definitions into an existing MIDCA implementation. From there, we will be able to perform experiments on existing domains. A second area is to develop more methodologies for each of the three anticipatory thinking steps. Expanding the failure sources beyond the failure inducing step (e.g. an action sequence) to identify the most parsimonious mitigation and extracting some benefit from unmitigated conditioning events are promising avenues of investigation.
Burns, E., and Ruml, J. B. W. 2012. Anticipatory On-Line Planning. ICAPS 333–337.
Coddington, A.; Fox, M.; Gough, J.; Long, D.; and Serina,