On the Structural Non-Preservation of Epistemic Behaviour under Policy Transformation
arXiv:2602.21424v1 Announce Type: new Abstract: Reinforcement learning (RL) agents under partial observability often condition actions on internally accumulated information such as memory or inferred latent context. We formalise such information-conditioned interaction patterns as behavioural dependency: variation in action selection with respect to internal information under fixed observations. This induces a probe-relative notion of $\epsilon$-behavioural equivalence and a within-policy behavioural distance that quantifies probe sensitivity. We establish three structural results. First, the set of policies exhibiting non-trivial behavioural dependency is not closed under convex aggregation. Second, behavioural distance contracts under convex combination. Third, we prove a sufficient local condition under which gradient ascent on a skewed mixture objective decreases behavioural distance when a dominant-mode gradient aligns with the direction of steepest contraction. Minimal bandit an
arXiv:2602.21424v1 Announce Type: new Abstract: Reinforcement learning (RL) agents under partial observability often condition actions on internally accumulated information such as memory or inferred latent context. We formalise such information-conditioned interaction patterns as behavioural dependency: variation in action selection with respect to internal information under fixed observations. This induces a probe-relative notion of $\epsilon$-behavioural equivalence and a within-policy behavioural distance that quantifies probe sensitivity. We establish three structural results. First, the set of policies exhibiting non-trivial behavioural dependency is not closed under convex aggregation. Second, behavioural distance contracts under convex combination. Third, we prove a sufficient local condition under which gradient ascent on a skewed mixture objective decreases behavioural distance when a dominant-mode gradient aligns with the direction of steepest contraction. Minimal bandit and partially observable gridworld experiments provide controlled witnesses of these mechanisms. In the examined settings, behavioural distance decreases under convex aggregation and under continued optimisation with skewed latent priors, and in these experiments it precedes degradation under latent prior shift. These results identify structural conditions under which probe-conditioned behavioural separation is not preserved under common policy transformations.
Executive Summary
This article presents a theoretical framework for understanding the impact of policy transformations on the preservation of epistemic behavior in reinforcement learning agents under partial observability. The authors introduce the concept of behavioural dependency, which measures the variation in action selection with respect to internal information under fixed observations. They demonstrate that the set of policies exhibiting non-trivial behavioural dependency is not closed under convex aggregation, and that behavioural distance contracts under convex combination. The authors also propose a sufficient local condition under which gradient ascent on a skewed mixture objective decreases behavioural distance. The article contributes to the understanding of the structural conditions under which probe-conditioned behavioural separation is not preserved under common policy transformations.
Key Points
- ▸ Introduction of behavioural dependency as a measure of variation in action selection with respect to internal information
- ▸ Demonstration of the non-closure of policies exhibiting non-trivial behavioural dependency under convex aggregation
- ▸ Establishment of the contraction of behavioural distance under convex combination
Merits
Strength
Development of a novel theoretical framework for understanding the impact of policy transformations on epistemic behavior
Strength
Contribution to the understanding of the structural conditions under which probe-conditioned behavioural separation is not preserved
Demerits
Limitation
Theoretical framework may be complex to apply in practice due to its abstract nature
Limitation
The study focuses on a limited set of scenarios and may not be generalizable to more complex environments
Expert Commentary
This article presents a significant contribution to the field of reinforcement learning, particularly in the area of epistemic behavior under partial observability. The authors' theoretical framework provides a novel perspective on the impact of policy transformations on the preservation of epistemic behavior. While the article's findings may be complex to apply in practice, they have the potential to inform the design of more robust reinforcement learning agents. Furthermore, the article's implications for policy-making in complex decision-making scenarios are significant and warrant further exploration.
Recommendations
- ✓ Future research should focus on developing more practical applications of the theoretical framework developed in this article
- ✓ Experimental studies should be conducted to validate the article's findings in more complex environments
