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AI Research
arXiv CS.AI·Jun 10·5 min read
Convergence of Monte Carlo Optimistic Policy Iteration: Beyond Uniform State-Action Updates
TL;DR
A significant challenge in Monte Carlo optimistic policy iteration (MC-O-PI) is ensuring convergence to optimal policies when the environment model is unknown. This paper introduces a relaxed condition for MC-O-PI, proving that it can converge even when updates are uniform only over actions within each state.
✦ Why It Matters
Engineers can implement more flexible Monte Carlo methods in complex environments without needing uniform state-action updates.
Key Takeaways
- Relax uniform initialization requirements for MC-O-PI.
- Implement updates uniformly over actions within states.
- Utilize mean-field dynamics for policy improvement.
- Explore other optimistic policy-iteration algorithms using this approach.
Full Summary
Monte Carlo optimistic policy iteration (MC-O-PI) traditionally requires uniform initialization across the entire state-action space to guarantee convergence to optimal policies, which is often impractical in real-world scenarios. This research relaxes that requirement, demonstrating that MC-O-PI can still achieve optimality if updates are uniform only among actions within each state.
The authors provide a proof that relies on mean-field dynamics, showing that policies improve monotonically under these conditions. They extend the classical lock-in argument to address the impact of noise on policy improvement.
This new approach not only enhances the understanding of MC-O-PI but also opens avenues for studying other optimistic policy-iteration algorithms. The findings suggest that more realistic implementations can be developed for environments with large or unknown state spaces, improving the applicability of reinforcement learning techniques.