We study the reinforcement learning for finite-horizon episodic Markov decision processes with adversarial reward and full information feedback, where the unknown transition probability function is a linear function of a given feature mapping. We propose an optimistic policy optimization algorithm with Bernstein bonus and show that it can achieve $\tilde{O}(dH\sqrt{T})$ regret, where $H$ is the length of the episode, $T$ is the number of interaction with the MDP and $d$ is the dimension of the feature mapping. Furthermore, we also prove a matching lower bound of $\tilde{\Omega}(dH\sqrt{T})$ up to logarithmic factors. To the best of our knowledge, this is the first computationally efficient, nearly minimax optimal algorithm for adversarial Markov decision processes with linear function approximation.

Policy gradient methods are widely used in solving two-player zero-sum games to achieve superhuman performance in practice. However, it remains elusive when they can provably find a near-optimal solution and how many samples and iterations are needed. The current paper studies natural extensions of Natural Policy Gradient algorithm for solving two-player zero-sum games where function approximation is used for generalization across states. We thoroughly characterize the algorithms' performance in terms of the number of samples, number of iterations, concentrability coefficients, and approximation error. To our knowledge, this is the first quantitative analysis of policy gradient methods with function approximation for two-player zero-sum Markov games.

With the digitalization of the economy and the advances in data analytics, firms are increasingly handing key manual decisions such as product pricing over to computers (Fisher et al., 2018; Miklós-Thal and Tucker, 2019; Hansen et al., 2020). However, the sophistication and powerfulness of algorithms have also led to another prominent concern on the possibility of collusion. Pricing algorithms may be too advanced to learn that it is optimal to collude (Ezrachi and Stucke, 2016). Although many are skeptical that autonomous collusion is only science fiction, recent experimental research (Waltman and Kaymak, 2008; Klein, 2019; Calvano et al., 2020; Hansen et al., 2020) suggests that dynamic pricing algorithms can learn collusive strategies from scratch, even without human guidance or communication with each other.

Data augmentation technique from computer vision has been widely considered as a regularization method to improve data efficiency and generalization performance in vision-based reinforcement learning. We variate the timing of using augmentation, which is, in turn, critical depending on tasks to be solved in training and testing. According to our experiments on Open AI Procgen Benchmark, if the regularization imposed by augmentation is helpful only in testing, it is better to procrastinate the augmentation after training than to use it during training in terms of sample and computation complexity. We note that some of such augmentations can disturb the training process. Conversely, an augmentation providing regularization useful in training needs to be used during the whole training period to fully utilize its benefit in terms of not only generalization but also data efficiency. These phenomena suggest a useful timing control of data augmentation in reinforcement learning.

Advances in Reinforcement Learning (RL) span a wide variety of applications which motivate development in this area. While application tasks serve as suitable benchmarks for real world problems, RL is seldomly used in practical scenarios consisting of abrupt dynamics. This allows one to rethink the problem setup in light of practical challenges. We present Trade Execution using Reinforcement Learning (TradeR) which aims to address two such practical challenges of catastrophy and surprise minimization by formulating trading as a real-world hierarchical RL problem. Through this lens, TradeR makes use of hierarchical RL to execute trade bids on high frequency real market experiences comprising of abrupt price variations during the 2019 fiscal year COVID19 stock market crash. The framework utilizes an energy-based scheme in conjunction with surprise value function for estimating and minimizing surprise. In a large-scale study of 35 stock symbols from the S&P500 index, TradeR demonstrates robustness to abrupt price changes and catastrophic losses while maintaining profitable outcomes. We hope that our work serves as a motivating example for application of RL to practical problems.

Safety is essential for reinforcement learning (RL) applied in real-world tasks like autonomous driving. Chance constraints which guarantee the satisfaction of state constraints at a high probability are suitable to represent the requirements in real-world environment with uncertainty. Existing chance constrained RL methods like the penalty method and the Lagrangian method either exhibit periodic oscillations or cannot satisfy the constraints. In this paper, we address these shortcomings by proposing a separated proportional-integral Lagrangian (SPIL) algorithm. Taking a control perspective, we first interpret the penalty method and the Lagrangian method as proportional feedback and integral feedback control, respectively. Then, a proportional-integral Lagrangian method is proposed to steady learning process while improving safety. To prevent integral overshooting and reduce conservatism, we introduce the integral separation technique inspired by PID control. Finally, an analytical gradient of the chance constraint is utilized for model-based policy optimization. The effectiveness of SPIL is demonstrated by a narrow car-following task. Experiments indicate that compared with previous methods, SPIL improves the performance while guaranteeing safety, with a steady learning process.

In large-scale systems there are fundamental challenges when centralised techniques are used for task allocation. The number of interactions is limited by resource constraints such as on computation, storage, and network communication. We can increase scalability by implementing the system as a distributed task-allocation system, sharing tasks across many agents. However, this also increases the resource cost of communications and synchronisation, and is difficult to scale. In this paper we present four algorithms to solve these problems. The combination of these algorithms enable each agent to improve their task allocation strategy through reinforcement learning, while changing how much they explore the system in response to how optimal they believe their current strategy is, given their past experience. We focus on distributed agent systems where the agents' behaviours are constrained by resource usage limits, limiting agents to local rather than system-wide knowledge. We evaluate these algorithms in a simulated environment where agents are given a task composed of multiple subtasks that must be allocated to other agents with differing capabilities, to then carry out those tasks. We also simulate real-life system effects such as networking instability. Our solution is shown to solve the task allocation problem to 6.7% of the theoretical optimal within the system configurations considered. It provides 5x better performance recovery over no-knowledge retention approaches when system connectivity is impacted, and is tested against systems up to 100 agents with less than a 9% impact on the algorithms' performance.

Epistemic uncertainty is the part of out-of-sample prediction error due to the lack of knowledge of the learner. Whereas previous work was focusing on model variance, we propose a principled approach for directly estimating epistemic uncertainty by learning to predict generalization error and subtracting an estimate of aleatoric uncertainty, i.e., intrinsic unpredictability. This estimator of epistemic uncertainty includes the effect of model bias and can be applied in non-stationary learning environments arising in active learning or reinforcement learning. In addition to demonstrating these properties of Direct Epistemic Uncertainty Prediction (DEUP), we illustrate its advantage against existing methods for uncertainty estimation on downstream tasks including sequential model optimization and reinforcement learning. We also evaluate the quality of uncertainty estimates from DEUP for probabilistic classification of images and for estimating uncertainty about synergistic drug combinations.

We study black-box reward poisoning attacks against reinforcement learning (RL), in which an adversary aims to manipulate the rewards to mislead a sequence of RL agents with unknown algorithms to learn a nefarious policy in an environment unknown to the adversary a priori. That is, our attack makes minimum assumptions on the prior knowledge of the adversary: it has no initial knowledge of the environment or the learner, and neither does it observe the learner's internal mechanism except for its performed actions. We design a novel black-box attack, U2, that can provably achieve a near-matching performance to the state-of-the-art white-box attack, demonstrating the feasibility of reward poisoning even in the most challenging black-box setting.

Generalization is a major challenge for multi-agent reinforcement learning. How well does an agent perform when placed in novel environments and in interactions with new co-players? In this paper, we investigate and quantify the relationship between generalization and diversity in the multi-agent domain. Across the range of multi-agent environments considered here, procedurally generating training levels significantly improves agent performance on held-out levels. However, agent performance on the specific levels used in training sometimes declines as a result. To better understand the effects of co-player variation, our experiments introduce a new environment-agnostic measure of behavioral diversity. Results demonstrate that population size and intrinsic motivation are both effective methods of generating greater population diversity. In turn, training with a diverse set of co-players strengthens agent performance in some (but not all) cases.