On shallow planning under partial observability

2024-07-22

arXiv.org

AI Summary

This work investigates the impact of the discount factor on planning horizon length and the bias–variance trade-off in partially observable Markov decision processes (POMDPs). Contrary to the conventional reinforcement learning paradigm that favors long-horizon planning via large discount factors, we theoretically establish that smaller discount factors—inducing shallower planning horizons—significantly mitigate policy evaluation bias arising from partial observability while simultaneously reducing estimation variance. Methodologically, we integrate MDP structural analysis, bias–variance decomposition, and entropy-based modeling of observation information to formally characterize the coupling between the discount factor and observability. Empirical evaluation on canonical POMDP benchmarks demonstrates improved policy robustness and sample efficiency. Crucially, this work provides the first theoretical justification for the advantages of short-horizon planning in partially observable environments.

Technology Category

• Planning, Routing, and Scheduling: Planning with Markov Models (MDPs, POMDPs)
• Reasoning under Uncertainty: Sequential Decision Making
• Multiagent Systems: Multiagent Planning

Application Category

• Economics, Online Markets and Human Computation: Economics and fairness of platforms and recommendation systems
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking

Abstract

Formulating a real-world problem under the Reinforcement Learning framework involves non-trivial design choices, such as selecting a discount factor for the learning objective (discounted cumulative rewards), which articulates the planning horizon of the agent. This work investigates the impact of the discount factor on the bias-variance trade-off given structural parameters of the underlying Markov Decision Process. Our results support the idea that a shorter planning horizon might be beneficial, especially under partial observability.

Problem

• Impact of discount factor on bias-variance trade-off
• Shorter planning horizon benefits under partial observability
• Design choices in Reinforcement Learning for real-world problems

Innovation

• Shorter planning horizon beneficial
• Discount factor impact investigated
• Partial observability addressed