We investigate multi-agent reinforcement learning for stochastic games with complex tasks, where the reward functions are non-Markovian. We utilize reward machines to incorporate high-level knowledge of complex tasks. We develop an algorithm called Q-learning with reward machines for stochastic games (QRM-SG), to learn the best-response strategy at Nash equilibrium for each agent. In QRM-SG, we define the Q-function at a Nash equilibrium in augmented state space. The augmented state space integrates the state of the stochastic game and the state of reward machines. Each agent learns the Q-functions of all agents in the system. We prove that Q-functions learned in QRM-SG converge to the Q-functions at a Nash equilibrium if the stage game at each time step during learning has a global optimum point or a saddle point, and the agents update Q-functions based on the best-response strategy at this point. We use the Lemke-Howson method to derive the best-response strategy given current Q-functions. The three case studies show that QRM-SG can learn the best-response strategies effectively. QRM-SG learns the best-response strategies after around 7500 episodes in Case Study I, 1000 episodes in Case Study II, and 1500 episodes in Case Study III, while baseline methods such as Nash Q-learning and MADDPG fail to converge to the Nash equilibrium in all three case studies.
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This work focuses on equilibrium selection in no-conflict multi-agent games, where we specifically study the problem of selecting a Pareto-optimal Nash equilibrium among several existing equilibria. It has been shown that many state-of-the-art multi-agent reinforcement learning (MARL) algorithms are prone to converging to Pareto-dominated equilibria due to the uncertainty each agent has about the policy of the other agents during training. To address sub-optimal equilibrium selection, we propose Pareto Actor-Critic (Pareto-AC), which is an actor-critic algorithm that utilises a simple property of no-conflict games (a superset of cooperative games): the Pareto-optimal equilibrium in a no-conflict game maximises the returns of all agents and, therefore, is the preferred outcome for all agents. We evaluate Pareto-AC in a diverse set of multi-agent games and show that it converges to higher episodic returns compared to seven state-of-the-art MARL algorithms and that it successfully converges to a Pareto-optimal equilibrium in a range of matrix games. Finally, we propose PACDCG, a graph neural network extension of Pareto-AC, which is shown to efficiently scale in games with a large number of agents.
In this work, a local Fourier analysis is presented to study the convergence of multigrid methods based on additive Schwarz smoothers. This analysis is presented as a general framework which allows us to study these smoothers for any type of discretization and problem. The presented framework is crucial in practice since it allows one to know a priori the answer to questions such as what is the size of the patch to use within these relaxations, the size of the overlapping, or even the optimal values for the weights involved in the smoother. Results are shown for a class of additive and restricted additive Schwarz relaxations used within a multigrid framework applied to high-order finite-element discretizations and saddle point problems, which are two of the contexts in which these type of relaxations are widely used.
Most Reinforcement Learning (RL) methods are traditionally studied in an active learning setting, where agents directly interact with their environments, observe action outcomes, and learn through trial and error. However, allowing partially trained agents to interact with real physical systems poses significant challenges, including high costs, safety risks, and the need for constant supervision. Offline RL addresses these cost and safety concerns by leveraging existing datasets and reducing the need for resource-intensive real-time interactions. Nevertheless, a substantial challenge lies in the demand for these datasets to be meticulously annotated with rewards. In this paper, we introduce Optimal Transport Reward (OTR) labelling, an innovative algorithm designed to assign rewards to offline trajectories, using a small number of high-quality expert demonstrations. The core principle of OTR involves employing Optimal Transport (OT) to calculate an optimal alignment between an unlabeled trajectory from the dataset and an expert demonstration. This alignment yields a similarity measure that is effectively interpreted as a reward signal. An offline RL algorithm can then utilize these reward signals to learn a policy. This approach circumvents the need for handcrafted rewards, unlocking the potential to harness vast datasets for policy learning. Leveraging the SurRoL simulation platform tailored for surgical robot learning, we generate datasets and employ them to train policies using the OTR algorithm. By demonstrating the efficacy of OTR in a different domain, we emphasize its versatility and its potential to expedite RL deployment across a wide range of fields.
We settle the sample complexity of policy learning for the maximization of the long run average reward associated with a uniformly ergodic Markov decision process (MDP), assuming a generative model. In this context, the existing literature provides a sample complexity upper bound of $\widetilde O(|S||A|t_{\text{mix}}^2 \epsilon^{-2})$ and a lower bound of $\Omega(|S||A|t_{\text{mix}} \epsilon^{-2})$. In these expressions, $|S|$ and $|A|$ denote the cardinalities of the state and action spaces respectively, $t_{\text{mix}}$ serves as a uniform upper limit for the total variation mixing times, and $\epsilon$ signifies the error tolerance. Therefore, a notable gap of $t_{\text{mix}}$ still remains to be bridged. Our primary contribution is to establish an estimator for the optimal policy of average reward MDPs with a sample complexity of $\widetilde O(|S||A|t_{\text{mix}}\epsilon^{-2})$, effectively reaching the lower bound in the literature. This is achieved by combining algorithmic ideas in Jin and Sidford (2021) with those of Li et al. (2020).
Distributed ensemble learning (DEL) involves training multiple models at distributed learners, and then combining their predictions to improve performance. Existing related studies focus on DEL algorithm design and optimization but ignore the important issue of incentives, without which self-interested learners may be unwilling to participate in DEL. We aim to fill this gap by presenting a first study on the incentive mechanism design for DEL. Our proposed mechanism specifies both the amount of training data and reward for learners with heterogeneous computation and communication costs. One design challenge is to have an accurate understanding regarding how learners' diversity (in terms of training data) affects the ensemble accuracy. To this end, we decompose the ensemble accuracy into a diversity-precision tradeoff to guide the mechanism design. Another challenge is that the mechanism design involves solving a mixed-integer program with a large search space. To this end, we propose an alternating algorithm that iteratively updates each learner's training data size and reward. We prove that under mild conditions, the algorithm converges. Numerical results using MNIST dataset show an interesting result: our proposed mechanism may prefer a lower level of learner diversity to achieve a higher ensemble accuracy.
Recently, contrastive learning has become a key component in fine-tuning code search models for software development efficiency and effectiveness. It pulls together positive code snippets while pushing negative samples away given search queries. Among contrastive learning, InfoNCE is the most widely used loss function due to its better performance. However, the following problems in negative samples of InfoNCE may deteriorate its representation learning: 1) The existence of false negative samples in large code corpora due to duplications. 2). The failure to explicitly differentiate between the potential relevance of negative samples. As an example, a bubble sorting algorithm example is less ``negative'' than a file saving function for the quick sorting algorithm query. In this paper, we tackle the above problems by proposing a simple yet effective Soft-InfoNCE loss that inserts weight terms into InfoNCE. In our proposed loss function, we apply three methods to estimate the weights of negative pairs and show that the vanilla InfoNCE loss is a special case of Soft-InfoNCE. Theoretically, we analyze the effects of Soft-InfoNCE on controlling the distribution of learnt code representations and on deducing a more precise mutual information estimation. We furthermore discuss the superiority of proposed loss functions with other design alternatives. Extensive experiments demonstrate the effectiveness of Soft-InfoNCE and weights estimation methods under state-of-the-art code search models on a large-scale public dataset consisting of six programming languages. Source code is available at \url{//github.com/Alex-HaochenLi/Soft-InfoNCE}.
In continual learning, the learner learns multiple tasks in sequence, with data being acquired only once for each task. Catastrophic forgetting is a major challenge to continual learning. To reduce forgetting, some existing rehearsal-based methods use episodic memory to replay samples of previous tasks. However, in the process of knowledge integration when learning a new task, this strategy also suffers from catastrophic forgetting due to an imbalance between old and new knowledge. To address this problem, we propose a novel replay strategy called Manifold Expansion Replay (MaER). We argue that expanding the implicit manifold of the knowledge representation in the episodic memory helps to improve the robustness and expressiveness of the model. To this end, we propose a greedy strategy to keep increasing the diameter of the implicit manifold represented by the knowledge in the buffer during memory management. In addition, we introduce Wasserstein distance instead of cross entropy as distillation loss to preserve previous knowledge. With extensive experimental validation on MNIST, CIFAR10, CIFAR100, and TinyImageNet, we show that the proposed method significantly improves the accuracy in continual learning setup, outperforming the state of the arts.
Recent contrastive representation learning methods rely on estimating mutual information (MI) between multiple views of an underlying context. E.g., we can derive multiple views of a given image by applying data augmentation, or we can split a sequence into views comprising the past and future of some step in the sequence. Contrastive lower bounds on MI are easy to optimize, but have a strong underestimation bias when estimating large amounts of MI. We propose decomposing the full MI estimation problem into a sum of smaller estimation problems by splitting one of the views into progressively more informed subviews and by applying the chain rule on MI between the decomposed views. This expression contains a sum of unconditional and conditional MI terms, each measuring modest chunks of the total MI, which facilitates approximation via contrastive bounds. To maximize the sum, we formulate a contrastive lower bound on the conditional MI which can be approximated efficiently. We refer to our general approach as Decomposed Estimation of Mutual Information (DEMI). We show that DEMI can capture a larger amount of MI than standard non-decomposed contrastive bounds in a synthetic setting, and learns better representations in a vision domain and for dialogue generation.
Promoting behavioural diversity is critical for solving games with non-transitive dynamics where strategic cycles exist, and there is no consistent winner (e.g., Rock-Paper-Scissors). Yet, there is a lack of rigorous treatment for defining diversity and constructing diversity-aware learning dynamics. In this work, we offer a geometric interpretation of behavioural diversity in games and introduce a novel diversity metric based on \emph{determinantal point processes} (DPP). By incorporating the diversity metric into best-response dynamics, we develop \emph{diverse fictitious play} and \emph{diverse policy-space response oracle} for solving normal-form games and open-ended games. We prove the uniqueness of the diverse best response and the convergence of our algorithms on two-player games. Importantly, we show that maximising the DPP-based diversity metric guarantees to enlarge the \emph{gamescape} -- convex polytopes spanned by agents' mixtures of strategies. To validate our diversity-aware solvers, we test on tens of games that show strong non-transitivity. Results suggest that our methods achieve much lower exploitability than state-of-the-art solvers by finding effective and diverse strategies.
Deep learning methods are achieving ever-increasing performance on many artificial intelligence tasks. A major limitation of deep models is that they are not amenable to interpretability. This limitation can be circumvented by developing post hoc techniques to explain the predictions, giving rise to the area of explainability. Recently, explainability of deep models on images and texts has achieved significant progress. In the area of graph data, graph neural networks (GNNs) and their explainability are experiencing rapid developments. However, there is neither a unified treatment of GNN explainability methods, nor a standard benchmark and testbed for evaluations. In this survey, we provide a unified and taxonomic view of current GNN explainability methods. Our unified and taxonomic treatments of this subject shed lights on the commonalities and differences of existing methods and set the stage for further methodological developments. To facilitate evaluations, we generate a set of benchmark graph datasets specifically for GNN explainability. We summarize current datasets and metrics for evaluating GNN explainability. Altogether, this work provides a unified methodological treatment of GNN explainability and a standardized testbed for evaluations.
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