Recently, neural heuristics based on deep reinforcement learning have exhibited promise in solving multi-objective combinatorial optimization problems (MOCOPs). However, they are still struggling to achieve high learning efficiency and solution quality. To tackle this issue, we propose an efficient meta neural heuristic (EMNH), in which a meta-model is first trained and then fine-tuned with a few steps to solve corresponding single-objective subproblems. Specifically, for the training process, a (partial) architecture-shared multi-task model is leveraged to achieve parallel learning for the meta-model, so as to speed up the training; meanwhile, a scaled symmetric sampling method with respect to the weight vectors is designed to stabilize the training. For the fine-tuning process, an efficient hierarchical method is proposed to systematically tackle all the subproblems. Experimental results on the multi-objective traveling salesman problem (MOTSP), multi-objective capacitated vehicle routing problem (MOCVRP), and multi-objective knapsack problem (MOKP) show that, EMNH is able to outperform the state-of-the-art neural heuristics in terms of solution quality and learning efficiency, and yield competitive solutions to the strong traditional heuristics while consuming much shorter time.

Most of existing neural methods for multi-objective combinatorial optimization (MOCO) problems solely rely on decomposition, which often leads to repetitive solutions for the respective subproblems, thus a limited Pareto set. Beyond decomposition, we propose a novel neural heuristic with diversity enhancement (NHDE) to produce more Pareto solutions from two perspectives. On the one hand, to hinder duplicated solutions for different subproblems, we propose an indicator-enhanced deep reinforcement learning method to guide the model, and design a heterogeneous graph attention mechanism to capture the relations between the instance graph and the Pareto front graph. On the other hand, to excavate more solutions in the neighborhood of each subproblem, we present a multiple Pareto optima strategy to sample and preserve desirable solutions. Experimental results on classic MOCO problems show that our NHDE is able to generate a Pareto front with higher diversity, thereby achieving superior overall performance. Moreover, our NHDE is generic and can be applied to different neural methods for MOCO.

In complex reinforcement learning (RL) problems, policies with similar rewards may have substantially different behaviors. It remains a fundamental challenge to optimize rewards while also discovering as many diverse strategies as possible, which can be crucial in many practical applications. Our study examines two design choices for tackling this challenge, i.e., diversity measure and computation framework. First, we find that with existing diversity measures, visually indistinguishable policies can still yield high diversity scores. To accurately capture the behavioral difference, we propose to incorporate the state-space distance information into the diversity measure. In addition, we examine two common computation frameworks for this problem, i.e., population-based training (PBT) and iterative learning (ITR). We show that although PBT is the precise problem formulation, ITR can achieve comparable diversity scores with higher computation efficiency, leading to improved solution quality in practice. Based on our analysis, we further combine ITR with two tractable realizations of the state-distance-based diversity measures and develop a novel diversity-driven RL algorithm, State-based Intrinsic-reward Policy Optimization (SIPO), with provable convergence properties. We empirically examine SIPO across three domains from robot locomotion to multi-agent games. In all of our testing environments, SIPO consistently produces strategically diverse and human-interpretable policies that cannot be discovered by existing baselines.

Bagging is an essential skill that humans perform in their daily activities. However, deformable objects, such as bags, are complex for robots to manipulate. This paper presents an efficient learning-based framework that enables robots to learn bagging. The novelty of this framework is its ability to perform bagging without relying on simulations. The learning process is accomplished through a reinforcement learning algorithm introduced in this work, designed to find the best grasping points of the bag based on a set of compact state representations. The framework utilizes a set of primitive actions and represents the task in five states. In our experiments, the framework reaches a 60 % and 80 % of success rate after around three hours of training in the real world when starting the bagging task from folded and unfolded, respectively. Finally, we test the trained model with two more bags of different sizes to evaluate its generalizability.

Reward design is a key component of deep reinforcement learning, yet some tasks and designer's objectives may be unnatural to define as a scalar cost function. Among the various techniques, formal methods integrated with DRL have garnered considerable attention due to their expressiveness and flexibility to define the reward and requirements for different states and actions of the agent. However, how to leverage Signal Temporal Logic (STL) to guide multi-agent reinforcement learning reward design remains unexplored. Complex interactions, heterogeneous goals and critical safety requirements in multi-agent systems make this problem even more challenging. In this paper, we propose a novel STL-guided multi-agent reinforcement learning framework. The STL requirements are designed to include both task specifications according to the objective of each agent and safety specifications, and the robustness values of the STL specifications are leveraged to generate rewards. We validate the advantages of our method through empirical studies. The experimental results demonstrate significant reward performance improvements compared to MARL without STL guidance, along with a remarkable increase in the overall safety rate of the multi-agent systems.

The field of safe multi-agent reinforcement learning, despite its potential applications in various domains such as drone delivery and vehicle automation, remains relatively unexplored. Training agents to learn optimal policies that maximize rewards while considering specific constraints can be challenging, particularly in scenarios where having a central controller to coordinate the agents during the training process is not feasible. In this paper, we address the problem of multi-agent policy optimization in a decentralized setting, where agents communicate with their neighbors to maximize the sum of their cumulative rewards while also satisfying each agent's safety constraints. We consider both peak and average constraints. In this scenario, there is no central controller coordinating the agents and both the rewards and constraints are only known to each agent locally/privately. We formulate the problem as a decentralized constrained multi-agent Markov Decision Problem and propose a momentum-based decentralized policy gradient method, DePAint, to solve it. To the best of our knowledge, this is the first privacy-preserving fully decentralized multi-agent reinforcement learning algorithm that considers both peak and average constraints. We also provide theoretical analysis and empirical evaluation of our algorithm in various scenarios and compare its performance to centralized algorithms that consider similar constraints.

In this paper we consider the problem of obtaining sharp bounds for the performance of temporal difference (TD) methods with linear functional approximation for policy evaluation in discounted Markov Decision Processes. We show that a simple algorithm with a universal and instance-independent step size together with Polyak-Ruppert tail averaging is sufficient to obtain near-optimal variance and bias terms. We also provide the respective sample complexity bounds. Our proof technique is based on refined error bounds for linear stochastic approximation together with the novel stability result for the product of random matrices that arise from the TD-type recurrence.

The boundary control problem is a non-convex optimization and control problem in many scientific domains, including fluid mechanics, structural engineering, and heat transfer optimization. The aim is to find the optimal values for the domain boundaries such that the enclosed domain adhering to the governing equations attains the desired state values. Traditionally, non-linear optimization methods, such as the Interior-Point method (IPM), are used to solve such problems. This project explores the possibilities of using deep learning and reinforcement learning to solve boundary control problems. We adhere to the framework of iterative optimization strategies, employing a spatial neural network to construct well-informed initial guesses, and a spatio-temporal neural network learns the iterative optimization algorithm using policy gradients. Synthetic data, generated from the problems formulated in the literature, is used for training, testing and validation. The numerical experiments indicate that the proposed method can rival the speed and accuracy of existing solvers. In our preliminary results, the network attains costs lower than IPOPT, a state-of-the-art non-linear IPM, in 51\% cases. The overall number of floating point operations in the proposed method is similar to that of IPOPT. Additionally, the informed initial guess method and the learned momentum-like behaviour in the optimizer method are incorporated to avoid convergence to local minima.

We propose a framework for the design of feedback controllers that combines the optimization-driven and model-free advantages of deep reinforcement learning with the stability guarantees provided by using the Youla-Kucera parameterization to define the search domain. Recent advances in behavioral systems allow us to construct a data-driven internal model; this enables an alternative realization of the Youla-Kucera parameterization based entirely on input-output exploration data. Perhaps of independent interest, we formulate and analyze the stability of such data-driven models in the presence of noise. The Youla-Kucera approach requires a stable "parameter" for controller design. For the training of reinforcement learning agents, the set of all stable linear operators is given explicitly through a matrix factorization approach. Moreover, a nonlinear extension is given using a neural network to express a parameterized set of stable operators, which enables seamless integration with standard deep learning libraries. Finally, we show how these ideas can also be applied to tune fixed-structure controllers.

Learning from demonstrations (LfD) has successfully trained robots to exhibit remarkable generalization capabilities. However, many powerful imitation techniques do not prioritize the feasibility of the robot behaviors they generate. In this work, we explore the feasibility of plans produced by LfD. As in prior work, we employ a temporal diffusion model with fixed start and goal states to facilitate imitation through in-painting. Unlike previous studies, we apply cold diffusion to ensure the optimization process is directed through the agent's replay buffer of previously visited states. This routing approach increases the likelihood that the final trajectories will predominantly occupy the feasible region of the robot's state space. We test this method in simulated robotic environments with obstacles and observe a significant improvement in the agent's ability to avoid these obstacles during planning.