Organizations: Linköping University, Linköping, Sweden · Ericsson Research, Stockholm, Sweden
Abstract
Reward machines (RMs) inform reinforcement learning agents about the reward structure of the environment, enabling support for non-Markovian tasks and improving sample efficiency. However, learning with RMs is ill-suited for long-horizon problems where subtasks can be completed in any order. In such cases, the amount of information to learn increases exponentially with the number of unordered subtasks. We address this issue by introducing three generalisations of RMs: (1) Numeric RMs allow users to express complex tasks in a compact form. (2) In agenda RMs, states are associated with an agenda that tracks the remaining subtasks to complete. (3) Coupled RMs have coupled states associated with each subtask in the agenda. In addition, we introduce QCoRM, a new task-decomposition Q-learning-based algorithm that leverages coupled RMs and preserves global optimality guarantees in tabular settings. Our experiments across four domains -- featuring both discrete and continuous action and state spaces -- demonstrate that QCoRM scales better than baseline algorithms for long-horizon problems with unordered subtasks.
We present Pareto Q-Learning with Reward Machines (PQLRM), a multi-objective reinforcement learning algorithm for tasks whose reward structure is specified by a set of reward machines (RMs). PQLRM combines Pareto Q-Learning (PQL), which maintains sets of vector-valued Q-estimates to approximate the Pareto front, with enhancements from Q-Learning with Reward Machines (QRM), which exploits the factored automaton structure of the reward signal. This yields a multi-policy algorithm that remains sample-efficient under non-Markovian, RM-encoded rewards. Experimental trials show that PQLRM converges faster than a naive PQL baseline applied to the cross-product MDP and can synthesize Pareto-optimal policies that QRM cannot.
Reinforcement learning algorithms are commonly analyzed (and designed) under the Markov assumption. This is unrealistic, as most environments encountered in practice are either partially observable, or require function approximation that restricts the agent to access non-Markovian state features. We consider the problem of learning an optimal reactive policy in a finite environment with deterministic observations (or equivalently, hard state aggregation). We introduce a new algorithm, Committed Q-learning, and prove almost-sure convergence to the optimal reactive policy under an intuitive assumption we call rewire-robustness. This assumption is strictly weaker than the q⋆-realizability condition used in prior work. Our algorithm is a variant of classical Q-learning in which the behavior policy commits to a single action upon entering a feature, and only resamples actions when the observed feature changes. A crucial part of our analysis is the introduction of quasi-Markov environments.
Reinforcement learning is a subfield of machine learning that studies how an agent interacts with an environment in order to extract as large a reward as possible. A standard approach to study such interaction is through Markov Decision Processes (MDPs) and the task of choosing an optimal policy --- a function that tells the agent which action to take. In this work, we study two types of MDPs --- finite-horizon and infinite-horizon discounted --- and propose new quantum algorithms for computing approximate optimal policies. Our quantum algorithms are based on a new combination of standard value iteration and quantum subroutines like quantum mean estimation and quantum maximum finding, overall enhanced with techniques from sample-optimal classical algorithms. Our resulting query complexities improve upon previous works, thus approaching already established quantum lower bounds.