Min-max optimization captures many important machine learning problems such as robust adversarial learning and inverse reinforcement learning, and nonconvex-strongly-concave min-max optimization has been an active line of research. Specifically, a novel variance reduction algorithm SREDA was proposed recently by (Luo et al. 2020) to solve such a problem, and was shown to achieve the optimal complexity dependence on the required accuracy level $\epsilon$. Despite the superior theoretical performance, the convergence guarantee of SREDA requires stringent initialization accuracy and an $\epsilon$-dependent stepsize for controlling the per-iteration progress, so that SREDA can run very slowly in practice. This paper develops a novel analytical framework that guarantees the SREDA's optimal complexity performance for a much enhanced algorithm SREDA-Boost, which has less restrictive initialization requirement and an accuracy-independent (and much bigger) stepsize. Hence, SREDA-Boost runs substantially faster in experiments than SREDA. We further apply SREDA-Boost to propose a zeroth-order variance reduction algorithm named ZO-SREDA-Boost for the scenario that has access only to the information about function values not gradients, and show that ZO-SREDA-Boost outperforms the best known complexity dependence on $\epsilon$. This is the first study that applies the variance reduction technique to zeroth-order algorithm for min-max optimization problems.

We solve active target tracking, one of the essential tasks in autonomous systems, using a deep reinforcement learning (RL) approach. In this problem, an autonomous agent is tasked with acquiring information about targets of interests using its onboard sensors. The classical challenges in this problem are system model dependence and the difficulty of computing information-theoretic cost functions for a long planning horizon. RL provides solutions for these challenges as the length of its effective planning horizon does not affect the computational complexity, and it drops the strong dependency of an algorithm on system models. In particular, we introduce Active Tracking Target Network (ATTN), a unified RL policy that is capable of solving major sub-tasks of active target tracking -- in-sight tracking, navigation, and exploration. The policy shows robust behavior for tracking agile and anomalous targets with a partially known target model. Additionally, the same policy is able to navigate in obstacle environments to reach distant targets as well as explore the environment when targets are positioned in unexpected locations.

We study the problem of least squares linear regression where the data-points are dependent and are sampled from a Markov chain. We establish sharp information theoretic minimax lower bounds for this problem in terms of $\tau_{\mathsf{mix}}$, the mixing time of the underlying Markov chain, under different noise settings. Our results establish that in general, optimization with Markovian data is strictly harder than optimization with independent data and a trivial algorithm (SGD-DD) that works with only one in every $\tilde{\Theta}(\tau_{\mathsf{mix}})$ samples, which are approximately independent, is minimax optimal. In fact, it is strictly better than the popular Stochastic Gradient Descent (SGD) method with constant step-size which is otherwise minimax optimal in the regression with independent data setting. Beyond a worst case analysis, we investigate whether structured datasets seen in practice such as Gaussian auto-regressive dynamics can admit more efficient optimization schemes. Surprisingly, even in this specific and natural setting, Stochastic Gradient Descent (SGD) with constant step-size is still no better than SGD-DD. Instead, we propose an algorithm based on experience replay--a popular reinforcement learning technique--that achieves a significantly better error rate. Our improved rate serves as one of the first results where an algorithm outperforms SGD-DD on an interesting Markov chain and also provides one of the first theoretical analyses to support the use of experience replay in practice.

In e-commerce markets, on time delivery is of great importance to customer satisfaction. In this paper, we present a Deep Reinforcement Learning (DRL) approach for deciding how and when orders should be batched and picked in a warehouse to minimize the number of tardy orders. In particular, the technique facilitates making decisions on whether an order should be picked individually (pick-by-order) or picked in a batch with other orders (pick-by-batch), and if so with which other orders. We approach the problem by formulating it as a semi-Markov decision process and develop a vector-based state representation that includes the characteristics of the warehouse system. This allows us to create a deep reinforcement learning solution that learns a strategy by interacting with the environment and solve the problem with a proximal policy optimization algorithm. We evaluate the performance of the proposed DRL approach by comparing it with several batching and sequencing heuristics in different problem settings. The results show that the DRL approach is able to develop a strategy that produces consistent, good solutions and performs better than the proposed heuristics.

Path Following and Collision Avoidance, be it for unmanned surface vessels or other autonomous vehicles, are two fundamental guidance problems in robotics. For many decades, they have been subject to academic study, leading to a vast number of proposed approaches. However, they have mostly been treated as separate problems, and have typically relied on non-linear first-principles models with parameters that can only be determined experimentally. The rise of Deep Reinforcement Learning (DRL) in recent years suggests an alternative approach: end-to-end learning of the optimal guidance policy from scratch by means of a trial-and-error based approach. In this article, we explore the potential of Proximal Policy Optimization (PPO), a DRL algorithm with demonstrated state-of-the-art performance on Continuous Control tasks, when applied to the dual-objective problem of controlling an underactuated Autonomous Surface Vehicle in a COLREGs compliant manner such that it follows an a priori known desired path while avoiding collisions with other vessels along the way. Based on high-fidelity elevation and AIS tracking data from the Trondheim Fjord, an inlet of the Norwegian sea, we evaluate the trained agent's performance in challenging, dynamic real-world scenarios where the ultimate success of the agent rests upon its ability to navigate non-uniform marine terrain while handling challenging, but realistic vessel encounters.

In this paper, we initiate the study of sample complexity of teaching, termed as "teaching dimension" (TDim) in the literature, for Q-learning. While the teaching dimension of supervised learning has been studied extensively, these results do not extend to reinforcement learning due to the temporal constraints posed by the underlying Markov Decision Process environment. We characterize the TDim of Q-learning under different teachers with varying control over the environment, and present matching optimal teaching algorithms. Our TDim results provide the minimum number of samples needed for reinforcement learning, thus complementing standard PAC-style RL sample complexity analysis. Our teaching algorithms have the potential to speed up RL agent learning in applications where a helpful teacher is available.

Non-stationarity arises in Reinforcement Learning (RL) even in stationary environments. Most RL algorithms collect new data throughout training, using a non-stationary behaviour policy. Furthermore, training targets in RL can change even with a fixed state distribution when the policy, critic, or bootstrap values are updated. We study these types of non-stationarity in supervised learning settings as well as in RL, finding that they can lead to worse generalisation performance when using deep neural network function approximators. Consequently, to improve generalisation of deep RL agents, we propose Iterated Relearning (ITER). ITER augments standard RL training by repeated knowledge transfer of the current policy into a freshly initialised network, which thereby experiences less non-stationarity during training. Experimentally, we show that ITER improves performance on the challenging generalisation benchmarks ProcGen and Multiroom.

In this paper, an online evolving framework is proposed to detect and revise a controller's imperfect decision-making in advance. The framework consists of three modules: the evolving Finite State Machine (e-FSM), action-reviser, and controller modules. The e-FSM module evolves a stochastic model (e.g., Discrete-Time Markov Chain) from scratch by determining new states and identifying transition probabilities repeatedly. With the latest stochastic model and given criteria, the action-reviser module checks validity of the controller's chosen action by predicting future states. Then, if the chosen action is not appropriate, another action is inspected and selected. In order to show the advantage of the proposed framework, the Deep Deterministic Policy Gradient (DDPG) w/ and w/o the online evolving framework are applied to control an ego-vehicle in the car-following scenario where control criteria are set by speed and safety. Experimental results show that inappropriate actions chosen by the DDPG controller are detected and revised appropriately through our proposed framework, resulting in no control failures after a few iterations.

Model-based reinforcement learning (MBRL) has shown its advantages in sample-efficiency over model-free reinforcement learning (MFRL). Despite the impressive results it achieves, it still faces a trade-off between the ease of data generation and model bias. In this paper, we propose a simple and elegant model-embedding model-based reinforcement learning (MEMB) algorithm in the framework of the probabilistic reinforcement learning. To balance the sample-efficiency and model bias, we exploit both real and imaginary data in the training. In particular, we embed the model in the policy update and learn $Q$ and $V$ functions from the real data set. We provide the theoretical analysis of MEMB with the Lipschitz continuity assumption on the model and policy. At last, we evaluate MEMB on several benchmarks and demonstrate our algorithm can achieve state-of-the-art performance.

Learning value functions off-policy is at the core of modern Reinforcement Learning (RL). Traditional off-policy actor-critic algorithms, however, only approximate the true policy gradient, since the gradient $\nabla_{\theta} Q^{\pi_{\theta}}(s,a)$ of the action-value function with respect to the policy parameters is often ignored. We introduce a class of value functions called Parameter-based Value Functions (PVFs) whose inputs include the policy parameters. PVFs can evaluate the performance of any policy given a state, a state-action pair, or a distribution over the RL agent's initial states. We show how PVFs yield exact policy gradient theorems. We derive off-policy actor-critic algorithms based on PVFs trained using Monte Carlo or Temporal Difference methods. Preliminary experimental results indicate that PVFs can effectively evaluate deterministic linear and nonlinear policies, outperforming state-of-the-art algorithms in the continuous control environment Swimmer-v3. Finally, we show how recurrent neural networks can be trained through PVFs to solve supervised and RL problems involving partial observability and long time lags between relevant events. This provides an alternative to backpropagation through time.