Finite memory methods improve decision making under uncertainty
Finite-Memory Control of POMDPs: Fundamental Limits and Efficient Design
Machine LearningInformation Theory
Summary
Making good decisions when you cannot fully observe the situation is very hard because it often requires remembering everything that happened before. The authors study how much memory you really need to perform nearly as well as possible, finding a theoretical limit on how well limited memory can do. They then create a method called RECAP that picks a smart, small set of memory states to store, helping control problems where you only get partial information. Their experiments show RECAP works better than other ways of managing limited memory on standard test problems.
What this means in practice
- •For robotics engineers: Build more efficient controllers that make near-optimal decisions with limited memory in robots operating with uncertain sensor data.
- •For autonomous vehicle developers: Design memory-limited controllers for managing uncertain driving environments that balance performance and computational resources.
Authors
Emrecan Kutay, Atilla Eryilmaz, Ness Shroff
Abstract
Optimal control of partially observable Markov decision processes (POMDPs), in general, requires a complete history. The belief state, a distribution over hidden states, summarizes this history and provides the classical sufficient statistic to control POMDPs. However, the continuous nature of the belief space generally prevents a finite-memory controller from maintaining it exactly. This raises the question we address in this work: what must the available finite memory preserve to achieve near-optimal control performance? We study this question through an information-theoretic converse that gives a fundamental lower bound on the loss of any finite-memory controller. The analysis introduces the concept of a decision witness that characterizes belief states whose confusion would lead to unavoidable loss. Motivated by this bound, we propose RECAP, a constructive quantization method for designing representative memory states. We prove an upper bound on the optimality gap of any RECAP codebook and use the components of this bound together with the converse analysis to define the codebook objective. Experiments on 11 POMDP benchmarks demonstrate that RECAP improves over finite-memory representation baselines under the same memory budget.