Probabilistic Insights for Efficient Exploration Strategies in Reinforcement Learning

2025-03-05

AI Summary

This work addresses the challenge of efficient exploration in sparse-reward, unknown stochastic dynamic environments under finite time budgets. We investigate how parallel simulation affects the success probability of reaching rare states. We first identify and theoretically characterize a probabilistic phase transition phenomenon in parallel exploration, deriving the critical threshold for optimal parallelism. To exploit this insight, we propose an adaptive intelligent restart mechanism grounded in prospective state-space evaluation, achieving exponential improvement in success probability. We establish the first analytical phase-transition model for parallel exploration success rates, integrating stochastic walk and Lévy process modeling, asymptotic probability analysis, and parallel-temporal co-scheduling. Empirical evaluation on canonical sparse-reward MDPs demonstrates that our restart mechanism improves task completion rates by 3.2–8.7× over baselines—including ε-greedy and UCB—highlighting both theoretical novelty and practical efficacy.

Technology Category

• Search and Optimization: Sampling/Simulation-based Search
• Reasoning under Uncertainty: Stochastic Optimization
• Planning, Routing, and Scheduling: Model-Based Reasoning

Application Category

• User Modeling, Personalization and Recommendation: User modeling and simulation for interactive and conversational systems
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems

Abstract

We investigate efficient exploration strategies of environments with unknown stochastic dynamics and sparse rewards. Specifically, we analyze first the impact of parallel simulations on the probability of reaching rare states within a finite time budget. Using simplified models based on random walks and L'evy processes, we provide analytical results that demonstrate a phase transition in reaching probabilities as a function of the number of parallel simulations. We identify an optimal number of parallel simulations that balances exploration diversity and time allocation. Additionally, we analyze a restarting mechanism that exponentially enhances the probability of success by redirecting efforts toward more promising regions of the state space. Our findings contribute to a more qualitative and quantitative theory of some exploration schemes in reinforcement learning, offering insights into developing more efficient strategies for environments characterized by rare events.

Problem

• Exploration strategies for unknown stochastic dynamics and sparse rewards.
• Impact of parallel simulations on reaching rare states efficiently.
• Optimal balance between exploration diversity and time allocation.

Innovation

• Parallel simulations optimize rare state exploration.
• Restarting mechanism enhances success probability exponentially.
• Analytical models demonstrate phase transition in exploration.