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Shapley Value Based Multi-Agent Reinforcement Learning: Theory, Method and Its Application to Energy Network
Feb 23, 2024
Multi-agent reinforcement learning is an area of rapid advancement in artificial intelligence and machine learning. One of the important questions to be answered is how to conduct credit assignment in a multi-agent system. There have been many schemes designed to conduct credit assignment by multi-agent reinforcement learning algorithms. Although these credit assignment schemes have been proved useful in improving the performance of multi-agent reinforcement learning, most of them are designed heuristically without a rigorous theoretic basis and therefore infeasible to understand how agents cooperate. In this thesis, we aim at investigating the foundation of credit assignment in multi-agent reinforcement learning via cooperative game theory. We first extend a game model called convex game and a payoff distribution scheme called Shapley value in cooperative game theory to Markov decision process, named as Markov convex game and Markov Shapley value respectively. We represent a global reward game as a Markov convex game under the grand coalition. As a result, Markov Shapley value can be reasonably used as a credit assignment scheme in the global reward game. Markov Shapley value possesses the following virtues: (i) efficiency; (ii) identifiability of dummy agents; (iii) reflecting the contribution and (iv) symmetry, which form the fair credit assignment. Based on Markov Shapley value, we propose three multi-agent reinforcement learning algorithms called SHAQ, SQDDPG and SMFPPO. Furthermore, we extend Markov convex game to partial observability to deal with the partially observable problems, named as partially observable Markov convex game. In application, we evaluate SQDDPG and SMFPPO on the real-world problem in energy networks.
Open Ad Hoc Teamwork with Cooperative Game Theory
Feb 23, 2024Ad hoc teamwork poses a challenging problem, requiring the design of an agent to collaborate with teammates without prior coordination or joint training. Open ad hoc teamwork further complicates this challenge by considering environments with a changing number of teammates, referred to as open teams. The state-of-the-art solution to this problem is graph-based policy learning (GPL), leveraging the generalizability of graph neural networks to handle an unrestricted number of agents and effectively address open teams. GPL's performance is superior to other methods, but its joint Q-value representation presents challenges for interpretation, hindering further development of this research line and applicability. In this paper, we establish a new theory to give an interpretation for the joint Q-value representation employed in GPL, from the perspective of cooperative game theory. Building on our theory, we propose a novel algorithm based on GPL framework, to complement the critical features that facilitate learning, but overlooked in GPL. Through experiments, we demonstrate the correctness of our theory by comparing the performance of the resulting algorithm with GPL in dynamic team compositions.
Aligning Individual and Collective Objectives in Multi-Agent Cooperation
Feb 19, 2024In the field of multi-agent learning, the challenge of mixed-motive cooperation is pronounced, given the inherent contradictions between individual and collective goals. Current research in this domain primarily focuses on incorporating domain knowledge into rewards or introducing additional mechanisms to foster cooperation. However, many of these methods suffer from the drawbacks of manual design costs and the lack of a theoretical grounding convergence procedure to the solution. To address this gap, we approach the mixed-motive game by modeling it as a differentiable game to study learning dynamics. We introduce a novel optimization method named Altruistic Gradient Adjustment (AgA) that employs gradient adjustments to novelly align individual and collective objectives. Furthermore, we provide theoretical proof that the selection of an appropriate alignment weight in AgA can accelerate convergence towards the desired solutions while effectively avoiding the undesired ones. The visualization of learning dynamics effectively demonstrates that AgA successfully achieves alignment between individual and collective objectives. Additionally, through evaluations conducted on established mixed-motive benchmarks such as the public good game, Cleanup, Harvest, and our modified mixed-motive SMAC environment, we validate AgA's capability to facilitate altruistic and fair collaboration.
E2E-AT: A Unified Framework for Tackling Uncertainty in Task-aware End-to-end Learning
Dec 23, 2023Successful machine learning involves a complete pipeline of data, model, and downstream applications. Instead of treating them separately, there has been a prominent increase of attention within the constrained optimization (CO) and machine learning (ML) communities towards combining prediction and optimization models. The so-called end-to-end (E2E) learning captures the task-based objective for which they will be used for decision making. Although a large variety of E2E algorithms have been presented, it has not been fully investigated how to systematically address uncertainties involved in such models. Most of the existing work considers the uncertainties of ML in the input space and improves robustness through adversarial training. We extend this idea to E2E learning and prove that there is a robustness certification procedure by solving augmented integer programming. Furthermore, we show that neglecting the uncertainty of COs during training causes a new trigger for generalization errors. To include all these components, we propose a unified framework that covers the uncertainties emerging in both the input feature space of the ML models and the COs. The framework is described as a robust optimization problem and is practically solved via end-to-end adversarial training (E2E-AT). Finally, the performance of E2E-AT is evaluated by a real-world end-to-end power system operation problem, including load forecasting and sequential scheduling tasks.
Semi-Supervised Dual-Stream Self-Attentive Adversarial Graph Contrastive Learning for Cross-Subject EEG-based Emotion Recognition
Aug 13, 2023
Electroencephalography (EEG) is an objective tool for emotion recognition with promising applications. However, the scarcity of labeled data remains a major challenge in this field, limiting the widespread use of EEG-based emotion recognition. In this paper, a semi-supervised Dual-stream Self-Attentive Adversarial Graph Contrastive learning framework (termed as DS-AGC) is proposed to tackle the challenge of limited labeled data in cross-subject EEG-based emotion recognition. The DS-AGC framework includes two parallel streams for extracting non-structural and structural EEG features. The non-structural stream incorporates a semi-supervised multi-domain adaptation method to alleviate distribution discrepancy among labeled source domain, unlabeled source domain, and unknown target domain. The structural stream develops a graph contrastive learning method to extract effective graph-based feature representation from multiple EEG channels in a semi-supervised manner. Further, a self-attentive fusion module is developed for feature fusion, sample selection, and emotion recognition, which highlights EEG features more relevant to emotions and data samples in the labeled source domain that are closer to the target domain. Extensive experiments conducted on two benchmark databases (SEED and SEED-IV) using a semi-supervised cross-subject leave-one-subject-out cross-validation evaluation scheme show that the proposed model outperforms existing methods under different incomplete label conditions (with an average improvement of 5.83% on SEED and 6.99% on SEED-IV), demonstrating its effectiveness in addressing the label scarcity problem in cross-subject EEG-based emotion recognition.
Semi-Centralised Multi-Agent Reinforcement Learning with Policy-Embedded Training
Sep 02, 2022
Centralised training (CT) is the basis for many popular multi-agent reinforcement learning (MARL) methods because it allows agents to quickly learn high-performing policies. However, CT relies on agents learning from one-off observations of other agents' actions at a given state. Because MARL agents explore and update their policies during training, these observations often provide poor predictions about other agents' behaviour and the expected return for a given action. CT methods therefore suffer from high variance and error-prone estimates, harming learning. CT methods also suffer from explosive growth in complexity due to the reliance on global observations, unless strong factorisation restrictions are imposed (e.g., monotonic reward functions for QMIX). We address these challenges with a new semi-centralised MARL framework that performs policy-embedded training and decentralised execution. Our method, policy embedded reinforcement learning algorithm (PERLA), is an enhancement tool for Actor-Critic MARL algorithms that leverages a novel parameter sharing protocol and policy embedding method to maintain estimates that account for other agents' behaviour. Our theory proves PERLA dramatically reduces the variance in value estimates. Unlike various CT methods, PERLA, which seamlessly adopts MARL algorithms, scales easily with the number of agents without the need for restrictive factorisation assumptions. We demonstrate PERLA's superior empirical performance and efficient scaling in benchmark environments including StarCraft Micromanagement II and Multi-agent Mujoco
Robust Reinforcement Learning in Continuous Control Tasks with Uncertainty Set Regularization
Jul 05, 2022
Reinforcement learning (RL) is recognized as lacking generalization and robustness under environmental perturbations, which excessively restricts its application for real-world robotics. Prior work claimed that adding regularization to the value function is equivalent to learning a robust policy with uncertain transitions. Although the regularization-robustness transformation is appealing for its simplicity and efficiency, it is still lacking in continuous control tasks. In this paper, we propose a new regularizer named $\textbf{U}$ncertainty $\textbf{S}$et $\textbf{R}$egularizer (USR), by formulating the uncertainty set on the parameter space of the transition function. In particular, USR is flexible enough to be plugged into any existing RL framework. To deal with unknown uncertainty sets, we further propose a novel adversarial approach to generate them based on the value function. We evaluate USR on the Real-world Reinforcement Learning (RWRL) benchmark, demonstrating improvements in the robust performance for perturbed testing environments.
Learning to Estimate and Refine Fluid Motion with Physical Dynamics
Jun 22, 2022
Extracting information on fluid motion directly from images is challenging. Fluid flow represents a complex dynamic system governed by the Navier-Stokes equations. General optical flow methods are typically designed for rigid body motion, and thus struggle if applied to fluid motion estimation directly. Further, optical flow methods only focus on two consecutive frames without utilising historical temporal information, while the fluid motion (velocity field) can be considered a continuous trajectory constrained by time-dependent partial differential equations (PDEs). This discrepancy has the potential to induce physically inconsistent estimations. Here we propose an unsupervised learning based prediction-correction scheme for fluid flow estimation. An estimate is first given by a PDE-constrained optical flow predictor, which is then refined by a physical based corrector. The proposed approach outperforms optical flow methods and shows competitive results compared to existing supervised learning based methods on a benchmark dataset. Furthermore, the proposed approach can generalize to complex real-world fluid scenarios where ground truth information is effectively unknowable. Finally, experiments demonstrate that the physical corrector can refine flow estimates by mimicking the operator splitting method commonly utilised in fluid dynamical simulation.
Multi-Agent Reinforcement Learning for Active Voltage Control on Power Distribution Networks
Nov 05, 2021
This paper presents a problem in power networks that creates an exciting and yet challenging real-world scenario for application of multi-agent reinforcement learning (MARL). The emerging trend of decarbonisation is placing excessive stress on power distribution networks. Active voltage control is seen as a promising solution to relieve power congestion and improve voltage quality without extra hardware investment, taking advantage of the controllable apparatuses in the network, such as roof-top photovoltaics (PVs) and static var compensators (SVCs). These controllable apparatuses appear in a vast number and are distributed in a wide geographic area, making MARL a natural candidate. This paper formulates the active voltage control problem in the framework of Dec-POMDP and establishes an open-source environment. It aims to bridge the gap between the power community and the MARL community and be a drive force towards real-world applications of MARL algorithms. Finally, we analyse the special characteristics of the active voltage control problems that cause challenges for state-of-the-art MARL approaches, and summarise the potential directions.
SHAQ: Incorporating Shapley Value Theory into Q-Learning for Multi-Agent Reinforcement Learning
May 31, 2021
Value factorisation proves to be a very useful technique in multi-agent reinforcement learning (MARL), but the underlying mechanism is not yet fully understood. This paper explores a theoretic basis for value factorisation. We generalise the Shapley value in the coalitional game theory to a Markov convex game (MCG) and use it to guide value factorisation in MARL. We show that the generalised Shapley value possesses several features such as (1) accurate estimation of the maximum global value, (2) fairness in the factorisation of the global value, and (3) being sensitive to dummy agents. The proposed theory yields a new learning algorithm called Sharpley Q-learning (SHAQ), which inherits the important merits of ordinary Q-learning but extends it to MARL. In comparison with prior-arts, SHAQ has a much weaker assumption (MCG) that is more compatible with real-world problems, but has superior explainability and performance in many cases. We demonstrated SHAQ and verified the theoretic claims on Predator-Prey and StarCraft Multi-Agent Challenge (SMAC).