How memory architecture affects learning in a simple POMDP: the two-hypothesis testing problem

TL;DR

This paper investigates how different memory architectures influence learning efficiency in a simple POMDP, demonstrating that constrained memory can improve training outcomes despite potential sacrifices in optimality.

Contribution

The study compares flexible and fixed memory architectures in a POMDP, showing constrained memory can achieve near-optimal performance and enhance training success.

Findings

Constrained memory architectures can match the performance of more flexible ones in a POMDP.

Training from random initialization is significantly more successful with fixed memory architectures.

Performance probability decreases exponentially with memory size, following a specific mathematical relation.

Abstract

Reinforcement learning is generally difficult for partially observable Markov decision processes (POMDPs), which occurs when the agent's observation is partial or noisy. To seek good performance in POMDPs, one strategy is to endow the agent with a finite memory, whose update is governed by the policy. However, policy optimization is non-convex in that case and can lead to poor training performance for random initialization. The performance can be empirically improved by constraining the memory architecture, then sacrificing optimality to facilitate training. Here we study this trade-off in a two-hypothesis testing problem, akin to the two-arm bandit problem. We compare two extreme cases: (i) the random access memory where any transitions between $M$ memory states are allowed and (ii) a fixed memory where the agent can access its last $m$ actions and rewards. For (i), the probability $q$ to play the worst arm is known to be exponentially small in $M$ for the optimal policy. Our main result is to show that similar performance can be reached for (ii) as well, despite the simplicity of the memory architecture: using a conjecture on Gray-ordered binary necklaces, we find policies for which $q$ is exponentially small in $2^m$, i.e. $q\sim\alpha^{2^m}$ with $\alpha < 1$. In addition, we observe empirically that training from random initialization leads to very poor results for (i), and significantly better results for (ii) thanks to the constraints on the memory architecture.