As reinforcement learning (RL) scales to solve increasingly complex tasks, interest continues to grow in the fields of AI safety and machine ethics. As a contribution to these fields, this paper introduces an extension to Deep Q-Networks (DQNs), called Empathic DQN, that is loosely inspired both by empathy and the golden rule ("Do unto others as you would have them do unto you"). Empathic DQN aims to help mitigate negative side effects to other agents resulting from myopic goal-directed behavior. We assume a setting where a learning agent coexists with other independent agents (who receive unknown rewards), where some types of reward (e.g. negative rewards from physical harm) may generalize across agents. Empathic DQN combines the typical (self-centered) value with the estimated value of other agents, by imagining (by its own standards) the value of it being in the other's situation (by considering constructed states where both agents are swapped). Proof-of-concept results in two gridworld environments highlight the approach's potential to decrease collateral harms. While extending Empathic DQN to complex environments is non-trivial, we believe that this first step highlights the potential of bridge-work between machine ethics and RL to contribute useful priors for norm-abiding RL agents.

Model-based reinforcement learning has the potential to be more sample efficient than model-free approaches. However, existing model-based methods are vulnerable to model bias, which leads to poor generalization and asymptotic performance compared to model-free counterparts. In addition, they are typically based on the model predictive control (MPC) framework, which not only is computationally inefficient at decision time but also does not enable policy transfer due to the lack of an explicit policy representation. In this paper, we propose a novel uncertainty-aware model-based policy optimization framework which solves those issues. In this framework, the agent simultaneously learns an uncertainty-aware dynamics model and optimizes the policy according to these learned models. In the optimization step, the policy gradient is computed by automatic differentiation through the models. With respect to sample efficiency alone, our approach shows promising results on challenging continuous control benchmarks with competitive asymptotic performance and significantly lower sample complexity than state-of-the-art baselines.

This paper is a broad and accessible survey of the methods we have at our disposal for Monte Carlo gradient estimation in machine learning and across the statistical sciences: the problem of computing the gradient of an expectation of a function with respect to parameters defining the distribution that is integrated; the problem of sensitivity analysis. In machine learning research, this gradient problem lies at the core of many learning problems, in supervised, unsupervised and reinforcement learning. We will generally seek to rewrite such gradients in a form that allows for Monte Carlo estimation, allowing them to be easily and efficiently used and analysed. We explore three strategies--the pathwise, score function, and measure-valued gradient estimators-- exploring their historical developments, derivation, and underlying assumptions. We describe their use in other fields, show how they are related and can be combined, and expand on their possible generalisations. Wherever Monte Carlo gradient estimators have been derived and deployed in the past, important advances have followed. A deeper and more widely-held understanding of this problem will lead to further advances, and it is these advances that we wish to support.

Stochastic mirror descent (SMD) keeps the advantages of simplicity of implementation, low memory requirement, and low computational complexity. However, the non-convexity of objective function with its non-stationary sampling process is the main bottleneck of applying SMD to reinforcement learning. To address the above problem, we propose the mirror policy optimization (MPO) by estimating the policy gradient via dynamic batch-size of gradient information. Comparing with REINFORCE or VPG, the proposed MPO improves the convergence rate from O(1/ N) to O(ln N/N). We also propose VRMPO algorithm, a variance reduction implementation of MPO. We prove the convergence of VRMPO and show its computational complexity. We evaluate the performance of VRMPO on the MuJoCo continuous control tasks, results show that VRMPO outperforms or matches several state-of-art algorithms DDPG, TRPO, PPO, and TD3.

Reinforcement Learning, a machine learning framework for training an autonomous agent based on rewards, has shown outstanding results in various domains. However, it is known that learning a good policy is difficult in a domain where rewards are rare. We propose a method, optimistic proximal policy optimization (OPPO) to alleviate this difficulty. OPPO considers the uncertainty of the estimated total return and optimistically evaluates the policy based on that amount. We show that OPPO outperforms the existing methods in a tabular task.

Off-policy learning is powerful for reinforcement learning. However, the high variance of off-policy evaluation is a critical challenge, which causes off-policy learning with function approximation falls into an uncontrolled instability. In this paper, for reducing the variance, we introduce control variate technique to Expected Sarsa($\lambda$) and propose a tabular ES($\lambda$)-CV algorithm. We prove that if a proper estimator of value function reaches, the proposed ES($\lambda$)-CV enjoys a lower variance than Expected Sarsa($\lambda$). Furthermore, to extend ES($\lambda$)-CV to be a convergent algorithm with linear function approximation, we propose the GES($\lambda$) algorithm under the convex-concave saddle-point formulation. We prove that the convergence rate of GES($\lambda$) achieves $\mathcal{O}(1/T)$, which matches or outperforms several state-of-art gradient-based algorithms, but we use a more relaxed step-size. Numerical experiments show that the proposed algorithm is stable and converges faster with lower variance than several state-of-art gradient-based TD learning algorithms: GQ($\lambda$), GTB($\lambda$) and ABQ($\zeta$).

Reinforcement learning agents that operate in diverse and complex environments can benefit from the structured decomposition of their behavior. Often, this is addressed in the context of hierarchical reinforcement learning, where the aim is to decompose a policy into lower-level primitives or options, and a higher-level meta-policy that triggers the appropriate behaviors for a given situation. However, the meta-policy must still produce appropriate decisions in all states. In this work, we propose a policy design that decomposes into primitives, similarly to hierarchical reinforcement learning, but without a high-level meta-policy. Instead, each primitive can decide for themselves whether they wish to act in the current state. We use an information-theoretic mechanism for enabling this decentralized decision: each primitive chooses how much information it needs about the current state to make a decision and the primitive that requests the most information about the current state acts in the world. The primitives are regularized to use as little information as possible, which leads to natural competition and specialization. We experimentally demonstrate that this policy architecture improves over both flat and hierarchical policies in terms of generalization.

In recent years, reinforcement learning has been successful in solving video games from Atari to Star Craft II. However, the end-to-end model-free reinforcement learning (RL) is not sample efficient and requires a significant amount of computational resources to achieve superhuman level performance. Model-free RL is also unlikely to produce human-like agents for playtesting and gameplaying AI in the development cycle of complex video games. In this paper, we present a hierarchical approach to training agents with the goal of achieving human-like style and high skill level in team sports games. While this is still work in progress, our preliminary results show that the presented approach holds promise for solving the posed multi-agent learning problem.

Sequential decision making in the presence of uncertainty and stochastic dynamics gives rise to distributions over state/action trajectories in reinforcement learning (RL) and optimal control problems. This observation has led to a variety of connections between RL and inference in probabilistic graphical models (PGMs). Here we explore a different dimension to this relationship, examining reinforcement learning using the tools and abstractions of statistical physics. The central object in the statistical physics abstraction is the idea of a partition function $\mathcal{Z}$, and here we construct a partition function from the ensemble of possible trajectories that an agent might take in a Markov decision process. Although value functions and $Q$-functions can be derived from this partition function and interpreted via average energies, the $\mathcal{Z}$-function provides an object with its own Bellman equation that can form the basis of alternative dynamic programming approaches. Moreover, when the MDP dynamics are deterministic, the Bellman equation for $\mathcal{Z}$ is linear, allowing direct solutions that are unavailable for the nonlinear equations associated with traditional value functions. The policies learned via these $\mathcal{Z}$-based Bellman updates are tightly linked to Boltzmann-like policy parameterizations. In addition to sampling actions proportionally to the exponential of the expected cumulative reward as Boltzmann policies would, these policies take entropy into account favoring states from which many outcomes are possible.

Liquidation is the process of selling a large number of shares of one stock sequentially within a given time frame, taking into consideration the costs arising from market impact and a trader's risk aversion. The main challenge in optimizing liquidation is to find an appropriate modeling system that can incorporate the complexities of the stock market and generate practical trading strategies. In this paper, we propose to use multi-agent deep reinforcement learning model, which better captures high-level complexities comparing to various machine learning methods, such that agents can learn how to make the best selling decisions. First, we theoretically analyze the Almgren and Chriss model and extend its fundamental mechanism so it can be used as the multi-agent trading environment. Our work builds the foundation for future multi-agent environment trading analysis. Secondly, we analyze the cooperative and competitive behaviours between agents by adjusting the reward functions for each agent, which overcomes the limitation of single-agent reinforcement learning algorithms. Finally, we simulate trading and develop an optimal trading strategy with practical constraints by using a reinforcement learning method, which shows the capabilities of reinforcement learning methods in solving realistic liquidation problems.