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# Characterizing Optimal Mixed Policies: Where to Intervene and What to Observe

NIPS 2020, (2020)

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Abstract

Intelligent agents are continuously faced with the challenge of optimizing a policy based on what they can observe (see) and which actions they can take (do) in the environment where they are deployed. Most policy can be parametrized in terms of these two dimensions, i.e., as a function of what can be seen and done given a certain situati...More

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Introduction

- Agents are deployed in complex and uncertain environments where they are bombarded with high volumes of information and are expected to operate efficiently, safely, and rationally.
- Given an MPS S, there always exists a deterministic mixed policy are disjoint and μ⇡
- Optimizing a mixed policy involves assessments of the effectiveness of its scope so that an agent can avoid intervening or observing on unnecessary actions or contexts.

Highlights

- Agents are deployed in complex and uncertain environments where they are bombarded with high volumes of information and are expected to operate efficiently, safely, and rationally
- We studied the space of mixed policies that emerges through the empowerment of an agent to determine the mode it will interact with the environment — i.e., which variables to intervene on and which contexts it decides to look into
- Facing new challenges to optimize this new mode of interaction, which has many additional degrees of freedom, we studied the topological structure induced by the different mixed policies, which could in turn be leveraged to determine partial orders across the policy space w.r.t. the maximum expected rewards achievable
- One of the surprising implications of this characterization provided here is that agents following a more standard approach may be hurting themselves, and may never be able to achieve an optimal performance regardless of the number of interactions performed
- Our results provide a tool for AI engineers and researchers to identify where the inefficiency of a policy may be coming from, including potentially unintended side effects
- It is not difficult to imagine that our work will share the common problems with other automated decision making tools and methods such as (i) the system optimized based on an ill-defined reward may harm ‘unknown unknowns’ or (ii) the optimization can be impossible due to the participants of adversarial players

Results

- The authors characterize the non-redundancy of MPS under optimality, which has practical implications to an agent adapting its suboptimal policy.
- Given hG, Y , X?, C?i, an MPS S is said to be non-redundant under optimality if there exists an SCM M compatible for every strictly subsumed
- Given a mixed policy ⇡ ⇠ S optimal with respect to S, if there exist decision rules {⇡0(x|(x0 [ ̇ c0) \ cx)}X2X0 such that yQ0x0 (y, c0)
- This follows from the definition of non-redundancy under optimality and expected reward.
- Given an MPS S, which satisfies non-redundancy (Thm. 1), let X0 ✓ X(S), actions of interest, C0 ( CX0 \X0.
- Given hG, X?, C?, Y i, let S be a set of NRO MPSes. An is said to be possibly-optimal if there exists such that μ⇤
- Refining the space of MPSes Equipped with the characterizations, the authors can refine the space of MPSes, the space of mixed policies, by filtering out MPSes that are either redundant or dominated by other MPS, eliciting a superset of POMPSes in a given setting.
- The authors investigate simplifying a mixed policy setting while preserving its POMPSes. First, one may think that the descendants of Y can be ignored since neither intervening action variables among them changes the reward nor observing contextualizable variables among them is feasible.
- The authors studied the space of mixed policies that emerges through the empowerment of an agent to determine the mode it will interact with the environment — i.e., which variables to intervene on and which contexts it decides to look into.

Conclusion

- Facing new challenges to optimize this new mode of interaction, which has many additional degrees of freedom, the authors studied the topological structure induced by the different mixed policies, which could in turn be leveraged to determine partial orders across the policy space w.r.t. the maximum expected rewards achievable.
- The authors provided a general characterization of the space of mixed policies with respect to properties that allow the agent to detect inefficient and suboptimal strategies.
- The current work does not consider multiple adversarial participants, which is a subject of future research

Summary

- Agents are deployed in complex and uncertain environments where they are bombarded with high volumes of information and are expected to operate efficiently, safely, and rationally.
- Given an MPS S, there always exists a deterministic mixed policy are disjoint and μ⇡
- Optimizing a mixed policy involves assessments of the effectiveness of its scope so that an agent can avoid intervening or observing on unnecessary actions or contexts.
- The authors characterize the non-redundancy of MPS under optimality, which has practical implications to an agent adapting its suboptimal policy.
- Given hG, Y , X?, C?i, an MPS S is said to be non-redundant under optimality if there exists an SCM M compatible for every strictly subsumed
- Given a mixed policy ⇡ ⇠ S optimal with respect to S, if there exist decision rules {⇡0(x|(x0 [ ̇ c0) \ cx)}X2X0 such that yQ0x0 (y, c0)
- This follows from the definition of non-redundancy under optimality and expected reward.
- Given an MPS S, which satisfies non-redundancy (Thm. 1), let X0 ✓ X(S), actions of interest, C0 ( CX0 \X0.
- Given hG, X?, C?, Y i, let S be a set of NRO MPSes. An is said to be possibly-optimal if there exists such that μ⇤
- Refining the space of MPSes Equipped with the characterizations, the authors can refine the space of MPSes, the space of mixed policies, by filtering out MPSes that are either redundant or dominated by other MPS, eliciting a superset of POMPSes in a given setting.
- The authors investigate simplifying a mixed policy setting while preserving its POMPSes. First, one may think that the descendants of Y can be ignored since neither intervening action variables among them changes the reward nor observing contextualizable variables among them is feasible.
- The authors studied the space of mixed policies that emerges through the empowerment of an agent to determine the mode it will interact with the environment — i.e., which variables to intervene on and which contexts it decides to look into.
- Facing new challenges to optimize this new mode of interaction, which has many additional degrees of freedom, the authors studied the topological structure induced by the different mixed policies, which could in turn be leveraged to determine partial orders across the policy space w.r.t. the maximum expected rewards achievable.
- The authors provided a general characterization of the space of mixed policies with respect to properties that allow the agent to detect inefficient and suboptimal strategies.
- The current work does not consider multiple adversarial participants, which is a subject of future research

Funding

- Acknowledgments and Disclosure of Funding This research is supported in parts by grants from NSF (IIS-1704352 and IIS-1750807 (CAREER))

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