Adaptive Agent Design

Reinforcement learning algorithms are commonly analyzed (and designed) under the Markov assumption. This is unrealistic, as most environments encountered in practice are either partially observable, or require function approximation that restricts the agent to access non-Markovian state features. We consider the problem of learning an optimal reactive policy in a finite environment with deterministic observations (or equivalently, hard state aggregation). We introduce a new algorithm, Committed Q-learning, and prove almost-sure convergence to the optimal reactive policy under an intuitive assumption we call rewire-robustness. This assumption is strictly weaker than the $q_\star$-realizability condition used in prior work. Our algorithm is a variant of classical Q-learning in which the behavior policy commits to a single action upon entering a feature, and only resamples actions when the observed feature changes. A crucial part of our analysis is the introduction of quasi-Markov environments.

We study what can be recovered about the transition probabilities of a Markov decision process from optimal actions alone. This is closely related to the inverse problem considered by Letcher et al., who ask when the dynamics can be recovered from numerical $Q$-values. Here the numerical values themselves are not observed; only the optimal actions are known, for every reward in a given class. For state-action rewards $r(s,a)$, knowing the optimal actions for every reward also tells us how much better one action is than another when each is followed by the same fixed policy. This is still not enough to determine the transition probabilities uniquely. We prove that two kernels give the same optimal actions for every reward exactly when $$Q_{s,a} = \Bigl(P_{s,a}+\tfrac1γe_s^{\mathsf T}(L-I)\Bigr)L^{-1}$$ for one invertible matrix $L$ satisfying $L\mathbf 1=\mathbf 1$. Near a kernel with strictly positive entries, there is an $n(n-1)$-dimensional family of different kernels with this property. The result is unchanged if we consider only rewards having a unique optimal action at every state. We then compare this with rewards of the forms $r(s)$ and $r(s,a,s')$. Rewards that depend on the next state can usually recover the transition kernel itself: every row at a state with at least two actions is determined, and we describe exactly when a row at a state with one action can remain hidden. State rewards reveal less: two kernels give the same optimal actions exactly when every deterministic policy is optimal for the same set of rewards. The results show how the form of the reward affects what can be learned about the dynamics from optimal actions alone.

We study policy optimization for online episodic tabular Markov decision processes with unknown transition kernels, aiming for best-of-both-worlds guarantees together with data-dependent regret bounds. Recent work (Dann et al., 2023; Li et al., 2026) has shown that policy optimization can adapt to both adversarial and stochastic losses with first-order, second-order, and path-length bounds, but only under known transitions, leaving open whether such data-dependent guarantees are achievable by policy optimization when the transition kernel is unknown. We resolve this by developing a new algorithm based on optimistic follow-the-regularized-leader that attains these guarantees under unknown transitions. The key ingredient is a new design of optimistic $Q$-function estimators together with a data-dependent transition bonus that controls estimator bias through the loss-prediction error. Our analysis further identifies an unavoidable transition-dependent complexity term that captures the intrinsic cost of estimating the transition kernel. As a result, we obtain first-order, second-order, and path-length bounds with the transition-dependent complexity term while simultaneously achieving gap-dependent $\mathrm{polylog}(T)$ regret in the stochastic regime.