Reward machines have recently been proposed as a means of encoding team tasks in cooperative multi-agent reinforcement learning. The resulting multi-agent reward machine is then decomposed into individual reward machines, one for each member of the team, allowing agents to learn in a decentralised manner while still achieving the team task. In this paper, we show how multi-agent reward machines for team tasks can be synthesised automatically from an abstraction of the environment in which the agents act and a high-level specification of the desired team behaviour expressed in a fragment of Alternating-time Temporal Logic. We present results from a number of benchmarks which suggest that our automated approach performs as well or better than reward machines in the literature.

Reward machines (RMs) are automata structures that encode (non-Markovian) reward functions for reinforcement learning (RL). RMs can reward any behaviour representable in regular languages and, when paired with RL algorithms that exploit RM structure, have been shown to significantly improve sample efficiency in many domains. In this work, we present pushdown reward machines (pdRMs), an extension of reward machines based on deterministic pushdown automata. pdRMs can recognise and reward temporally extended behaviours representable in deterministic context-free languages, making them more expressive than reward machines. We introduce two variants of pdRM-based policies, one which has access to the entire stack of the pdRM, and one which can only access the top k symbols (for a given constant k) of the stack. We propose a procedure to check when the two kinds of policies (for a given environment, pdRM, and constant k) achieve the same optimal state values. We then provide theoretical results establishing the expressive power of pdRMs, and space complexity results for the proposed learning problems. Lastly, we propose an approach for off-policy RL algorithms that exploits counterfactual experiences with pdRMs. We conclude by providing experimental results showing how agents can be trained to perform tasks representable in deterministic context-free languages using pdRMs.

We present Pure-Past Action Masking (PPAM), a lightweight approach to action masking for safe reinforcement learning. In PPAM, actions are disallowed (“masked”) according to specifications expressed in Pure-Past Linear Temporal Logic (PPLTL). PPAM can enforce non-Markovian constraints, i.e., constraints based on the history of the system, rather than just the current state of the (possibly hidden) MDP. The features used in the safety constraint need not be the same as those used by the learning agent, allowing a clear separation of concerns between the safety constraints and reward specifications of the (learning) agent. We prove formally that an agent trained with PPAM can learn any optimal policy that satisfies the safety constraints, and that they are as expressive as shields, another approach to enforce non-Markovian constraints in RL. Finally, we provide empirical results showing how PPAM can guarantee constraint satisfaction in practice.

Reward machines allow the definition of rewards for temporally extended tasks and behaviors. Specifying “informative” reward machines can be challenging. One way to address this is to generate reward machines from a high-level abstract description of the learning environment, using techniques such as AI planning. However, previous planning-based approaches generate a reward machine based on a single (sequential or partial-order) plan, and do not allow maximum flexibility to the learning agent. In this paper we propose a new approach to synthesising reward machines which is based on the set of partial order plans for a goal. We prove that learning using such “maximally permissive” reward machines results in higher rewards than learning using RMs based on a single plan. We present experimental results which support our theoretical claims by showing that our approach obtains higher rewards than the single-plan approach in practice.

Reward machines have recently been proposed as a means of encoding team tasks in cooperative multi-agent reinforcement learning. The resulting multi-agent reward machine is then decomposed into individual reward machines, one for each member of the team, allowing agents to learn in a decentralised manner while still achieving the team task. In this paper, we show how multi-agent reward machines for team tasks can be synthesised automatically from an abstraction of the environment in which the agents act and a high-level specification of the desired team behaviour expressed in a fragment of Alternating-time Temporal Logic. We present results from a number of benchmarks which suggest that our automated approach performs as well or better than reward machines in the literature.