Multi-Agent Reinforcement Learning for Adaptive Mesh Refinement

Adaptive mesh refinement (AMR) is necessary for efficient finite element simulations of complex physical phenomenon, as it allocates limited computational budget based on the need for higher or lower resolution, which varies over space and time. We present a novel formulation of AMR as a fully-cooperative Markov game, in which each element is an independent agent who makes refinement and de-refinement choices based on local information. We design a novel deep multi-agent reinforcement learning (MARL) algorithm called Value Decomposition Graph Network (VDGN), which solves the two core challenges that AMR poses for MARL: posthumous credit assignment due to agent creation and deletion, and unstructured observations due to the diversity of mesh geometries. For the first time, we show that MARL enables anticipatory refinement of regions that will encounter complex features at future times, thereby unlocking entirely new regions of the error-cost objective landscape that are inaccessible by traditional methods based on local error estimators. Comprehensive experiments show that VDGN policies significantly outperform error threshold-based policies in global error and cost metrics. We show that learned policies generalize to test problems with physical features, mesh geometries, and longer simulation times that were not seen in training. We also extend VDGN with multi-objective optimization capabilities to find the Pareto front of the tradeoff between cost and error.

Do Deep Neural Networks Always Perform Better When Eating More Data?

Data has now become a shortcoming of deep learning. Researchers in their own fields share the thinking that "deep neural networks might not always perform better when they eat more data," which still lacks experimental validation and a convincing guiding theory. Here to fill this lack, we design experiments from Identically Independent Distribution(IID) and Out of Distribution(OOD), which give powerful answers. For the purpose of guidance, based on the discussion of results, two theories are proposed: under IID condition, the amount of information determines the effectivity of each sample, the contribution of samples and difference between classes determine the amount of sample information and the amount of class information; under OOD condition, the cross-domain degree of samples determine the contributions, and the bias-fitting caused by irrelevant elements is a significant factor of cross-domain. The above theories provide guidance from the perspective of data, which can promote a wide range of practical applications of artificial intelligence.

Permutation Invariant Policy Optimization for Mean-Field Multi-Agent Reinforcement Learning: A Principled Approach

Multi-agent reinforcement learning (MARL) becomes more challenging in the presence of more agents, as the capacity of the joint state and action spaces grows exponentially in the number of agents. To address such a challenge of scale, we identify a class of cooperative MARL problems with permutation invariance, and formulate it as a mean-field Markov decision processes (MDP). To exploit the permutation invariance therein, we propose the mean-field proximal policy optimization (MF-PPO) algorithm, at the core of which is a permutation-invariant actor-critic neural architecture. We prove that MF-PPO attains the globally optimal policy at a sublinear rate of convergence. Moreover, its sample complexity is independent of the number of agents. We validate the theoretical advantages of MF-PPO with numerical experiments in the multi-agent particle environment (MPE). In particular, we show that the inductive bias introduced by the permutation-invariant neural architecture enables MF-PPO to outperform existing competitors with a smaller number of model parameters, which is the key to its generalization performance.

Reinforcement Learning for Adaptive Mesh Refinement

Large-scale finite element simulations of complex physical systems governed by partial differential equations crucially depend on adaptive mesh refinement (AMR) to allocate computational budget to regions where higher resolution is required. Existing scalable AMR methods make heuristic refinement decisions based on instantaneous error estimation and thus do not aim for long-term optimality over an entire simulation. We propose a novel formulation of AMR as a Markov decision process and apply deep reinforcement learning (RL) to train refinement policies directly from simulation. AMR poses a new problem for RL in that both the state dimension and available action set changes at every step, which we solve by proposing new policy architectures with differing generality and inductive bias. The model sizes of these policy architectures are independent of the mesh size and hence scale to arbitrarily large and complex simulations. We demonstrate in comprehensive experiments on static function estimation and the advection of different fields that RL policies can be competitive with a widely-used error estimator and generalize to larger, more complex, and unseen test problems.

GraphOpt: Learning Optimization Models of Graph Formation

Formation mechanisms are fundamental to the study of complex networks, but learning them from observations is challenging. In real-world domains, one often has access only to the final constructed graph, instead of the full construction process, and observed graphs exhibit complex structural properties. In this work, we propose GraphOpt, an end-to-end framework that jointly learns an implicit model of graph structure formation and discovers an underlying optimization mechanism in the form of a latent objective function. The learned objective can serve as an explanation for the observed graph properties, thereby lending itself to transfer across different graphs within a domain. GraphOpt poses link formation in graphs as a sequential decision-making process and solves it using maximum entropy inverse reinforcement learning algorithm. Further, it employs a novel continuous latent action space that aids scalability. Empirically, we demonstrate that GraphOpt discovers a latent objective transferable across graphs with different characteristics. GraphOpt also learns a robust stochastic policy that achieves competitive link prediction performance without being explicitly trained on this task and further enables construction of graphs with properties similar to those of the observed graph.

Learning to Incentivize Other Learning Agents

The challenge of developing powerful and general Reinforcement Learning (RL) agents has received increasing attention in recent years. Much of this effort has focused on the single-agent setting, in which an agent maximizes a predefined extrinsic reward function. However, a long-term question inevitably arises: how will such independent agents cooperate when they are continually learning and acting in a shared multi-agent environment? Observing that humans often provide incentives to influence others' behavior, we propose to equip each RL agent in a multi-agent environment with the ability to give rewards directly to other agents, using a learned incentive function. Each agent learns its own incentive function by explicitly accounting for its impact on the learning of recipients and, through them, the impact on its own extrinsic objective. We demonstrate in experiments that such agents significantly outperform standard RL and opponent-shaping agents in challenging general-sum Markov games, often by finding a near-optimal division of labor. Our work points toward more opportunities and challenges along the path to ensure the common good in a multi-agent future.

Hierarchical Cooperative Multi-Agent Reinforcement Learning with Skill Discovery

Human players in professional team sports achieve high level coordination by dynamically choosing complementary skills and executing primitive actions to perform these skills. As a step toward creating intelligent agents with this capability for fully cooperative multi-agent settings, we propose a two-level hierarchical multi-agent reinforcement learning (MARL) algorithm with unsupervised skill discovery. Agents learn useful and distinct skills at the low level via independent Q-learning, while they learn to select complementary latent skill variables at the high level via centralized multi-agent training with an extrinsic team reward. The set of low-level skills emerges from an intrinsic reward that solely promotes the decodability of latent skill variables from the trajectory of a low-level skill, without the need for hand-crafted rewards for each skill. For scalable decentralized execution, each agent independently chooses latent skill variables and primitive actions based on local observations. Our overall method enables the use of general cooperative MARL algorithms for training high level policies and single-agent RL for training low level skills. Experiments on a stochastic high dimensional team game show the emergence of useful skills and cooperative team play. The interpretability of the learned skills show the promise of the proposed method for achieving human-AI cooperation in team sports games.

Single Episode Policy Transfer in Reinforcement Learning

Transfer and adaptation to new unknown environmental dynamics is a key challenge for reinforcement learning (RL). An even greater challenge is performing near-optimally in a single attempt at test time, possibly without access to dense rewards, which is not addressed by current methods that require multiple experience rollouts for adaptation. To achieve single episode transfer in a family of environments with related dynamics, we propose a general algorithm that optimizes a probe and an inference model to rapidly estimate underlying latent variables of test dynamics, which are then immediately used as input to a universal control policy. This modular approach enables integration of state-of-the-art algorithms for variational inference or RL. Moreover, our approach does not require access to rewards at test time, allowing it to perform in settings where existing adaptive approaches cannot. In diverse experimental domains with a single episode test constraint, our method significantly outperforms existing adaptive approaches and shows favorable performance against baselines for robust transfer.

Integrating independent and centralized multi-agent reinforcement learning for traffic signal network optimization

Traffic congestion in metropolitan areas is a world-wide problem that can be ameliorated by traffic lights that respond dynamically to real-time conditions. Recent studies applying deep reinforcement learning (RL) to optimize single traffic lights have shown significant improvement over conventional control. However, optimization of global traffic condition over a large road network fundamentally is a cooperative multi-agent control problem, for which single-agent RL is not suitable due to environment non-stationarity and infeasibility of optimizing over an exponential joint-action space. Motivated by these challenges, we propose QCOMBO, a simple yet effective multi-agent reinforcement learning (MARL) algorithm that combines the advantages of independent and centralized learning. We ensure scalability by selecting actions from individually optimized utility functions, which are shaped to maximize global performance via a novel consistency regularization loss between individual utility and a global action-value function. Experiments on diverse road topologies and traffic flow conditions in the SUMO traffic simulator show competitive performance of QCOMBO versus recent state-of-the-art MARL algorithms. We further show that policies trained on small sub-networks can effectively generalize to larger networks under different traffic flow conditions, providing empirical evidence for the suitability of MARL for intelligent traffic control.

CM3: Cooperative Multi-goal Multi-stage Multi-agent Reinforcement Learning

We propose CM3, a new deep reinforcement learning method for cooperative multi-agent problems where agents must coordinate for joint success in achieving different individual goals. We restructure multi-agent learning into a two-stage curriculum, consisting of a single-agent stage for learning to accomplish individual tasks, followed by a multi-agent stage for learning to cooperate in the presence of other agents. These two stages are bridged by modular augmentation of neural network policy and value functions. We further adapt the actor-critic framework to this curriculum by formulating local and global views of the policy gradient and learning via a double critic, consisting of a decentralized value function and a centralized action-value function. We evaluated CM3 on a new high-dimensional multi-agent environment with sparse rewards: negotiating lane changes among multiple autonomous vehicles in the Simulation of Urban Mobility (SUMO) traffic simulator. Detailed ablation experiments show the positive contribution of each component in CM3, and the overall synthesis converges significantly faster to higher performance policies than existing cooperative multi-agent methods.