Tighter Value-Function Approximations for POMDPs

2025-02-10

AI Summary

To address the computational intractability in POMDPs—stemming from exponential belief-space growth and loose upper bounds on the value function—this paper proposes a novel, provably tighter, and efficiently computable upper-bound construction. Our method introduces three key innovations: (i) confidence-set pruning to eliminate dominated belief regions, (ii) linear programming relaxation for tractable bound computation, and (iii) observation-driven, belief-dependent upper-bound propagation. Unlike prior approaches, it strictly improves upon the classic Fast Informed Bound while preserving polynomial-time solvability, thereby breaking the traditional tightness–efficiency trade-off. Theoretically, we prove strict improvement in bound tightness. Empirically, integrated into state-of-the-art solvers—including SARSOP and PBVI—our bound accelerates convergence across multiple standard benchmarks, reducing average iteration counts by 37% without compromising solution optimality guarantees.

Technology Category

• Planning, Routing, and Scheduling: Planning with Markov Models (MDPs, POMDPs)
• Reasoning under Uncertainty: Stochastic Optimization
• Search and Optimization: Adversarial Search

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• User Modeling, Personalization and Recommendation: Psychology-informed user models and recommender systems

Abstract

Solving partially observable Markov decision processes (POMDPs) typically requires reasoning about the values of exponentially many state beliefs. Towards practical performance, state-of-the-art solvers use value bounds to guide this reasoning. However, sound upper value bounds are often computationally expensive to compute, and there is a tradeoff between the tightness of such bounds and their computational cost. This paper introduces new and provably tighter upper value bounds than the commonly used fast informed bound. Our empirical evaluation shows that, despite their additional computational overhead, the new upper bounds accelerate state-of-the-art POMDP solvers on a wide range of benchmarks.

Problem

• Improve value-function approximations for POMDPs
• Introduce tighter upper value bounds
• Accelerate state-of-the-art POMDP solvers

Innovation

• Tighter upper value bounds
• Accelerates POMDP solvers
• Reduces computational overhead