aiqbench analysis
This research resolves a long-standing theoretical barrier in reinforcement learning by proving that Monte Carlo optimistic policy iteration converges to optimality even without uniform initialization across the entire state-action space. By relaxing the impractical requirement for uniform state updates, the authors enable more realistic implementations where episodes start in arbitrary states, provided action updates remain uniform within each state. The novel proof technique, which adapts stability-ODE methods to handle non-commutative dynamics, offers a new analytical framework for studying optimistic policy-iteration algorithms in general.
Convergence of Monte Carlo Optimistic Policy Iteration: Beyond Uniform State-Action Updates
arXiv:2606.10580v1 Announce Type: new Abstract: The asymptotic behaviour of Monte Carlo optimistic policy iteration (MC-O-PI) is a long-standing open question. When the model of the environment is unknown, as is common in practice, the only known condition that guarantees convergence to optimality is impractical. In its canonical form, this condition requires that the episodes used for policy evaluation be initialised uniformly over the entire state-action space. This paper strictly relaxes that requirement. Specifically, we prove that initial-visit MC-O-PI converges to optimality even when updates are uniform only over the actions within each state. This allows episodes to start in different states at arbitrary frequencies; a realistic implementation when the state space is large or unknown but the action space in each state is manageable. The proof departs from the classical analysis of Tsitsiklis whose central commutativity argument no longer applies when states are updated at different frequencies. Instead, we first show that the mean-field dynamics of MC-O-PI generate monotonically improving policies when updates are uniform over the actions in each state, and then prove that noise cannot consistently prevent this improvement by extending the lock-in argument of the combined stability-ODE method. This approach suggests a new way to study optimistic policy-iteration algorithms in general.
Abstract:The asymptotic behaviour of Monte Carlo optimistic policy iteration (MC-O-PI) is a long-standing open question. When the model of the environment is unknown, as is common in practice, the only known condition that guarantees convergence to optimality is impractical. In its canonical form, this condition requires that the episodes used for policy evaluation be initialised uniformly over the entire state-action space. This paper strictly relaxes that requirement. Specifically, we prove that initial-visit MC-O-PI converges to optimality even when updates are uniform only over the actions within each state. This allows episodes to start in different states at arbitrary frequencies; a realistic implementation when the state space is large or unknown but the action space in each state is manageable. The proof departs from the classical analysis of Tsitsiklis whose central commutativity argument no longer applies when states are updated at different frequencies. Instead, we first show that the mean-field dynamics of MC-O-PI generate monotonically improving policies when updates are uniform over the actions in each state, and then prove that noise cannot consistently prevent this improvement by extending the lock-in argument of the combined stability-ODE method. This approach suggests a new way to study optimistic policy-iteration algorithms in general.
Machine Learning (cs.LG); Artificial Intelligence (cs.AI)
arXiv:2606.10580 [cs.LG]
(or arXiv:2606.10580v1 [cs.LG] for this version)
https://doi.org/10.48550/arXiv.2606.10580 Focus to learn more arXiv-issued DOI via DataCite (pending registration)
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