An Adversarial Interpretation of Information-Theoretic Bounded Rationality

Recently, there has been a growing interest in modeling planning with information constraints. Accordingly, an agent maximizes a regularized expected utility known as the free energy, where the regularizer is given by the information divergence from a prior to a posterior policy. While this approach can be justified in various ways, including from statistical mechanics and information theory, it is still unclear how it relates to decision-making against adversarial environments. This connection has previously been suggested in work relating the free energy to risk-sensitive control and to extensive form games. Here, we show that a single-agent free energy optimization is equivalent to a game between the agent and an imaginary adversary. The adversary can, by paying an exponential penalty, generate costs that diminish the decision maker’s payoffs. It turns out that the optimal strategy of the adversary consists in choosing costs so as to render the decision maker indifferent among its choices, which is a definining property of a Nash equilibrium, thus tightening the connection between free energy optimization and game theory.

💡 Research Summary

The paper investigates the relationship between the information‑theoretic (IT) bounded rationality framework—specifically the free‑energy objective—and decision‑making in adversarial environments. Classical AI planning is based on expected utility maximization, which yields a linear objective and a deterministic optimal policy that requires exhaustive evaluation of all actions. In contrast, IT bounded rationality introduces a regularization term in the form of a Kullback‑Leibler (KL) divergence between a prior policy (p_0) and a posterior policy (p). The resulting free‑energy functional
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