Deep Neural Networks and Reinforcement Learning methods have empirically shown great promise in tackling challenging combinatorial problems. In those methods a deep neural network is used as a solution generator which is then trained by gradient-based methods (e.g., policy gradient) to successively obtain better solution distributions.In this work we introduce a novel theoretical framework for analyzing the effectiveness of such methods. We ask whether there exist generative models that (i) are expressive enough to generate approximately optimal solutions; (ii) have a tractable, i.e, polynomial in the size of the input, number of parameters; (iii) their optimization landscape is benign in the sense that it does not contain sub-optimal stationary points. Our main contribution is a positive answer to this question.

In this work, we conduct an extensive empirical study of several deep reinforcement learning algorithms on two challenging combinatorial optimization problems: the job-shop and flexible job-shop scheduling problems, both fundamental challenges with multiple industrial applications. Broadly, deep reinforcement learning algorithms fall into two categories: policy-gradient and value-based. While value-based algorithms have achieved notable success in domains such as the Arcade Learning Environment, the combinatorial optimization community has predominantly favored policy-gradient algorithms, often overlooking the potential of value-based alternatives. From our results, value-based algorithms demonstrated a lower variance and a more stable convergence profile compared to policy-gradient ones. Moreover, they achieved superior cross-size and cross-distribution generalization, that is, effectively solving instances that are substantially larger or structurally distinct from those seen during training. Finally, our analysis also suggests that the relative performance of each category of algorithms may be dependent on structural properties of the problem, such as problem flexibility and instance size. Overall, our findings challenge the prevailing assumption that policy-gradient algorithms are inherently superior for combinatorial optimization. We show instead that value-based algorithms can match or even surpass the performance of policy-gradient algorithms, suggesting that they deserve greater attention from the combinatorial optimization community. Our code is openly available at: https://github.com/AJ-Correa/Unraveling-the-Rainbow

Deep Neural Networks and Reinforcement Learning methods have empirically shown great promise in tackling challenging combinatorial problems. In those methods a deep neural network is used as a solution generator which is then trained by gradient-based methods (e.g., policy gradient) to successively obtain better solution distributions.In this work we introduce a novel theoretical framework for analyzing the effectiveness of such methods. We ask whether there exist generative models that (i) are expressive enough to generate approximately optimal solutions; (ii) have a tractable, i.e, polynomial in the size of the input, number of parameters; (iii) their optimization landscape is benign in the sense that it does not contain sub-optimal stationary points. Our main contribution is a positive answer to this question. As a byproduct of our analysis we introduce a novel regularization process over vanilla gradient descent and provide theoretical and experimental evidence that it helps address vanishing-gradient issues and escape bad stationary points.

Stochastic networks and queueing systems often lead to Markov decision processes (MDPs) with large state and action spaces as well as nonconvex objective functions, which hinders the convergence of many reinforcement learning (RL) algorithms. Policy-gradient methods perform well on MDPs with large state and action spaces, but they sometimes experience slow convergence due to the high variance of the gradient estimator. In this paper, we show that some of these difficulties can be circumvented by exploiting the structure of the underlying MDP. We first introduce a new family of gradient estimators called score-aware gradient estimators (SAGEs). When the stationary distribution of the MDP belongs to an exponential family parametrized by the policy parameters, SAGEs allow us to estimate the policy gradient without relying on value-function estimation, contrary to classical policy-gradient methods like actor-critic. To demonstrate their applicability, we examine two common control problems arising in stochastic networks and queueing systems whose stationary distributions have a product-form, a special case of exponential families. As a second contribution, we show that, under appropriate assumptions, the policy under a SAGE-based policy-gradient method has a large probability of converging to an optimal policy, provided that it starts sufficiently close to it, even with a nonconvex objective function and multiple maximizers. Our key assumptions are that, locally around a maximizer, a nondegeneracy property of the Hessian of the objective function holds and a Lyapunov function exists. Finally, we conduct a numerical comparison between a SAGE-based policy-gradient method and an actor-critic algorithm. The results demonstrate that the SAGE-based method finds close-to-optimal policies more rapidly, highlighting its superior performance over the traditional actor-critic method.

Multi-agent pathfinding (MAPF) is a critical field in many large-scale robotic applications, often being the fundamental step in multi-agent systems. The increasing complexity of MAPF in complex and crowded environments, however, critically diminishes the effectiveness of existing solutions. In contrast to other studies that have either presented a general overview of the recent advancements in MAPF or extensively reviewed Deep Reinforcement Learning (DRL) within multi-agent system settings independently, our work presented in this review paper focuses on highlighting the integration of DRL-based approaches in MAPF. Moreover, we aim to bridge the current gap in evaluating MAPF solutions by addressing the lack of unified evaluation metrics and providing comprehensive clarification on these metrics. Finally, our paper discusses the potential of model-based DRL as a promising future direction and provides its required foundational understanding to address current challenges in MAPF. Our objective is to assist readers in gaining insight into the current research direction, providing unified metrics for comparing different MAPF algorithms and expanding their knowledge of model-based DRL to address the existing challenges in MAPF.

Probabilistic temporal planning attempts to find good policies for acting in domains with concurrent durative tasks, multiple uncertain outcomes, and limited resources. These domains are typically modelled as Markov decision problems and solved using dynamic programming methods. This paper demonstrates the application of reinforcement learning -- in the form of a policy-gradient method -- to these domains. Our emphasis is large domains that are infeasible for dynamic programming. Our ap- proach is to construct simple policies, or agents, for each planning task.

Probabilistic temporal planning attempts to find good policies for acting in domains with concurrent durative tasks, multiple uncertain outcomes, and limited resources. These domains are typically modelled as Markov decision problems and solved using dynamic programming methods. This paper demonstrates the application of reinforcement learning -- in the form of a policy-gradient method -- to these domains. Our emphasis is large domains that are infeasible for dynamic programming. Our approach is to construct simple policies, or agents, for each planning task. The result is a general probabilistic temporal planner, named the Factored Policy-Gradient Planner (FPG-Planner), which can handle hundreds of tasks, optimising for probability of success, duration, and resource use.

Probabilistic temporal planning attempts to find good policies for acting in domains with concurrent durative tasks, multiple uncertain outcomes, and limited resources. These domains are typically modelled as Markov decision problems and solved using dynamic programming methods. This paper demonstrates the application of reinforcement learning -- in the form of a policy-gradient method -- to these domains. Our emphasis is large domains that are infeasible for dynamic programming. Our approach is to construct simple policies, or agents, for each planning task. The result is a general probabilistic temporal planner, named the Factored Policy-Gradient Planner (FPG-Planner), which can handle hundreds of tasks, optimising for probability of success, duration, and resource use.

Probabilistic temporal planning attempts to find good policies for acting in domains with concurrent durative tasks, multiple uncertain outcomes, and limited resources. These domains are typically modelled as Markov decision problems and solved using dynamic programming methods. This paper demonstrates the application of reinforcement learning -- in the form of a policy-gradient method -- to these domains. Our emphasis is large domains that are infeasible for dynamic programming. Our approach isto construct simple policies, or agents, for each planning task. The result is a general probabilistic temporal planner, named the Factored Policy-Gradient Planner (FPG-Planner), which can handle hundreds of tasks, optimising for probability of success, duration, and resource use.