We present an end-to-end framework for solving the Vehicle Routing Problem (VRP) using reinforcement learning. In this approach, we train a single policy model that finds near-optimal solutions for a broad range of problem instances of similar size, only by observing the reward signals and following feasibility rules. We consider a parameterized stochastic policy, and by applying a policy gradient algorithm to optimize its parameters, the trained model produces the solution as a sequence of consecutive actions in real time, without the need to re-train for every new problem instance. On capacitated VRP, our approach outperforms classical heuristics and Google's OR-Tools on medium-sized instances in solution quality with comparable computation time (after training). We demonstrate how our approach can handle problems with split delivery and explore the effect of such deliveries on the solution quality.

Despite the success of single-agent reinforcement learning, multi-agent reinforcement learning (MARL) remains challenging due to complex interactions between agents. Motivated by decentralized applications such as sensor networks, swarm robotics, and power grids, we study policy evaluation in MARL, where agents with jointly observed state-action pairs and private local rewards collaborate to learn the value of a given policy. In this paper, we propose a double averaging scheme, where each agent iteratively performs averaging over both space and time to incorporate neighboring gradient information and local reward information, respectively. We prove that the proposed algorithm converges to the optimal solution at a global geometric rate. In particular, such an algorithm is built upon a primal-dual reformulation of the mean squared Bellman error minimization problem, which gives rise to a decentralized convex-concave saddle-point problem.

Potential based reward shaping is a powerful technique for accelerating convergence of reinforcement learning algorithms. Typically, such information includes an estimate of the optimal value function and is often provided by a human expert or other sources of domain knowledge. However, this information is often biased or inaccurate and can mislead many reinforcement learning algorithms. In this paper, we apply Bayesian Model Combination with multiple experts in a way that learns to trust a good combination of experts as training progresses. This approach is both computationally efficient and general, and is shown numerically to improve convergence across discrete and continuous domains and different reinforcement learning algorithms.

Deep reinforcement learning could be used to learn dexterous robotic policies but it is challenging to transfer them to new robots with vastly different hardware properties. It is also prohibitively expensive to learn a new policy from scratch for each robot hardware due to the high sample complexity of modern state-of-the-art algorithms. We propose a novel approach called Hardware Conditioned Policies where we train a universal policy conditioned on a vector representation of robot hardware. We considered robots in simulation with varied dynamics, kinematic structure, kinematic lengths and degrees-of-freedom. First, we use the kinematic structure directly as the hardware encoding and show great zero-shot transfer to completely novel robots not seen during training.

We interpret meta-reinforcement learning as the problem of learning how to quickly find a good sampling distribution in a new environment. This interpretation leads to the development of two new meta-reinforcement learning algorithms: E-MAML and E-$\text{RL} 2$. Results are presented on a new environment we call Krazy World': a difficult high-dimensional gridworld which is designed to highlight the importance of correctly differentiating through sampling distributions in meta-reinforcement learning. Further results are presented on a set of maze environments. We show E-MAML and E-$\text{RL} 2$ deliver better performance than baseline algorithms on both tasks.

We propose a framework for ensuring safe behavior of a reinforcement learning agent when the reward function may be difficult to specify. In order to do this, we rely on the existence of demonstrations from expert policies, and we provide a theoretical framework for the agent to optimize in the space of rewards consistent with its existing knowledge. We propose two methods to solve the resulting optimization: an exact ellipsoid-based method and a method in the spirit of the "follow-the-perturbed-leader" algorithm. Our experiments demonstrate the behavior of our algorithm in both discrete and continuous problems. The trained agent safely avoids states with potential negative effects while imitating the behavior of the expert in the other states.

Multitask reinforcement learning (MTRL) suffers from scalability issues when the number of tasks or trajectories grows large. The main reason behind this drawback is the reliance on centeralised solutions. Recent methods exploited the connection between MTRL and general consensus to propose scalable solutions. These methods, however, suffer from two drawbacks. First, they rely on predefined objectives, and, second, exhibit linear convergence guarantees.

We address reinforcement learning problems with finite state and action spaces where the underlying MDP has some known structure that could be potentially exploited to minimize the exploration rates of suboptimal (state, action) pairs. For any arbitrary structure, we derive problem-specific regret lower bounds satisfied by any learning algorithm. These lower bounds are made explicit for unstructured MDPs and for those whose transition probabilities and average reward functions are Lipschitz continuous w.r.t. the state and action. For Lipschitz MDPs, the bounds are shown not to scale with the sizes S and A of the state and action spaces, i.e., they are smaller than c log T where T is the time horizon and the constant c only depends on the Lipschitz structure, the span of the bias function, and the minimal action sub-optimality gap. This contrasts with unstructured MDPs where the regret lower bound typically scales as SA log T. We devise DEL (Directed Exploration Learning), an algorithm that matches our regret lower bounds.

We introduce a theorem proving algorithm that uses practically no domain heuristics for guiding its connection-style proof search. Instead, it runs many Monte-Carlo simulations guided by reinforcement learning from previous proof attempts. We produce several versions of the prover, parameterized by different learning and guiding algorithms. The strongest version of the system is trained on a large corpus of mathematical problems and evaluated on previously unseen problems. The trained system solves within the same number of inferences over 40% more problems than a baseline prover, which is an unusually high improvement in this hard AI domain.

The design of a reward function often poses a major practical challenge to real-world applications of reinforcement learning. Approaches such as inverse reinforcement learning attempt to overcome this challenge, but require expert demonstrations, which can be difficult or expensive to obtain in practice. We propose inverse event-based control, which generalizes inverse reinforcement learning methods to cases where full demonstrations are not needed, such as when only samples of desired goal states are available. Our method is grounded in an alternative perspective on control and reinforcement learning, where an agent's goal is to maximize the probability that one or more events will happen at some point in the future, rather than maximizing cumulative rewards. We demonstrate the effectiveness of our methods on continuous control tasks, with a focus on high-dimensional observations like images where rewards are hard or even impossible to specify.