We study the regret of reinforcement learning from offline data generated by a fixed behavior policy in an infinite-horizon discounted Markov decision process (MDP). While existing analyses of common approaches, such as fitted $Q$-iteration (FQI), suggest a $O(1/\sqrt{n})$ convergence for regret, empirical behavior exhibits much faster convergence. In this paper, we present a finer regret analysis that exactly characterizes this phenomenon by providing fast rates for the regret convergence. First, we show that given any estimate for the optimal quality function $Q^*$, the regret of the policy it defines converges at a rate given by the exponentiation of the $Q^*$-estimate's pointwise convergence rate, thus speeding it up. The level of exponentiation depends on the level of noise in the decision-making problem, rather than the estimation problem. We establish such noise levels for linear and tabular MDPs as examples. Second, we provide new analyses of FQI and Bellman residual minimization to establish the correct pointwise convergence guarantees. As specific cases, our results imply $O(1/n)$ regret rates in linear cases and $\exp(-\Omega(n))$ regret rates in tabular cases.

This paper studies the control synthesis of motion planning subject to uncertainties. The uncertainties are considered in robot motion and environment properties, giving rise to the probabilistic labeled Markov decision process (MDP). A model-free reinforcement learning (RL) is developed to generate a finite-memory control policy to satisfy high-level tasks expressed in linear temporal logic (LTL) formulas. One of the novelties is to translate LTL into a limit deterministic generalized B\"uchi automaton (LDGBA) and develop a corresponding embedded LDGBA (E-LDGBA) by incorporating a tracking-frontier function to overcome the issue of sparse accepting rewards, resulting in improved learning performance without increasing computational complexity. Due to potentially conflicting tasks, a relaxed product MDP is developed to allow the agent to revise its motion plan without strictly following the desired LTL constraints if the desired tasks can only be partially fulfilled. An expected return composed of violation rewards and accepting rewards is developed. The designed violation function quantifies the differences between the revised and the desired motion planning, while the accepting rewards are designed to enforce the satisfaction of the acceptance condition of the relaxed product MDP. Rigorous analysis shows that any RL algorithm that optimizes the expected return is guaranteed to find policies that, in decreasing order, can 1) satisfy acceptance condition of relaxed product MDP and 2) reduce the violation cost over long-term behaviors. Also, we validate the control synthesis approach via simulation and experimental results.

This paper studies the exponential stability of random matrix products driven by a general (possibly unbounded) state space Markov chain. It is a cornerstone in the analysis of stochastic algorithms in machine learning (e.g. for parameter tracking in online learning or reinforcement learning). The existing results impose strong conditions such as uniform boundedness of the matrix-valued functions and uniform ergodicity of the Markov chains. Our main contribution is an exponential stability result for the $p$-th moment of random matrix product, provided that (i) the underlying Markov chain satisfies a super-Lyapunov drift condition, (ii) the growth of the matrix-valued functions is controlled by an appropriately defined function (related to the drift condition). Using this result, we give finite-time $p$-th moment bounds for constant and decreasing stepsize linear stochastic approximation schemes with Markovian noise on general state space. We illustrate these findings for linear value-function estimation in reinforcement learning. We provide finite-time $p$-th moment bound for various members of temporal difference (TD) family of algorithms.

In online advertising, recommender systems try to propose items from a list of products to potential customers according to their interests. Such systems have been increasingly deployed in E-commerce due to the rapid growth of information technology and availability of large datasets. The ever-increasing progress in the field of artificial intelligence has provided powerful tools for dealing with such real-life problems. Deep reinforcement learning (RL) that deploys deep neural networks as universal function approximators can be viewed as a valid approach for design and implementation of recommender systems. This paper provides a comparative study between value-based and policy-based deep RL algorithms for designing recommender systems for online advertising. The RecoGym environment is adopted for training these RL-based recommender systems, where the long short term memory (LSTM) is deployed to build value and policy networks in these two approaches, respectively. LSTM is used to take account of the key role that order plays in the sequence of item observations by users. The designed recommender systems aim at maximising the click-through rate (CTR) for the recommended items. Finally, guidelines are provided for choosing proper RL algorithms for different scenarios that the recommender system is expected to handle.

Hierarchical reinforcement learning approaches learn policies based on hierarchical decision structures. However, training such methods in practice may lead to poor generalization, with either sub-policies executing actions for too few time steps or devolving into a single policy altogether. In our work, we introduce an alternative approach to sequentially learn such skills without using an overarching hierarchical policy, in the context of environments in which an objective of the agent is to prolong the episode for as long as possible, or in other words `stay alive'. We demonstrate the utility of our approach in a simulated 3D navigation environment which we have built. We show that our method outperforms prior methods such as Soft Actor Critic and Soft Option Critic on our environment, as well as the Atari River Raid environment.

A Machine Learning interview calls for a rigorous interview process where the candidates are judged on various aspects such as technical and programming skills, knowledge of methods and clarity of basic concepts. If you aspire to apply for machine learning jobs, it is crucial to know what kind of interview questions generally recruiters and hiring managers may ask. This is an attempt to help you crack the machine learning interviews at major product based companies and start-ups. Usually, machine learning interviews at major companies require a thorough knowledge of data structures and algorithms. In the upcoming series of articles, we shall start from the basics of concepts and build upon these concepts to solve major interview questions. Machine learning interviews comprise of many rounds, which begin with a screening test. This comprises solving questions either on the white-board, or solving it on online platforms like HackerRank, LeetCode etc. Here, we have compiled a list of ...

Many tasks that we do on a regular basis, such as navigating a city, cooking a meal, or loading a dishwasher, require planning over extended periods of time. Accomplishing these tasks may seem simple to us; however, reasoning over long time horizons remains a major challenge for today's Reinforcement Learning (RL) algorithms. While unable to plan over long horizons, deep RL algorithms excel at learning policies for short horizon tasks, such as robotic grasping, directly from pixels. At the same time, classical planning methods such as Dijkstra's algorithm and A search can plan over long time horizons, but they require hand-specified or task-specific abstract representations of the environment as input. To achieve the best of both worlds, state-of-the-art visual navigation methods have applied classical search methods to learned graphs.

The current work is motivated by the need for robust statistical methods for precision medicine; as such, we address the need for statistical methods that provide actionable inference for a single unit at any point in time. We aim to learn an optimal, unknown choice of the controlled components of the design in order to optimize the expected outcome; with that, we adapt the randomization mechanism for future time-point experiments based on the data collected on the individual over time. Our results demonstrate that one can learn the optimal rule based on a single sample, and thereby adjust the design at any point t with valid inference for the mean target parameter. This work provides several contributions to the field of statistical precision medicine. First, we define a general class of averages of conditional causal parameters defined by the current context for the single unit time-series data. We define a nonparametric model for the probability distribution of the time-series under few assumptions, and aim to fully utilize the sequential randomization in the estimation procedure via the double robust structure of the efficient influence curve of the proposed target parameter. We present multiple exploration-exploitation strategies for assigning treatment, and methods for estimating the optimal rule. Lastly, we present the study of the data-adaptive inference on the mean under the optimal treatment rule, where the target parameter adapts over time in response to the observed context of the individual. Our target parameter is pathwise differentiable with an efficient influence function that is doubly robust - which makes it easier to estimate than previously proposed variations. We characterize the limit distribution of our estimator under a Donsker condition expressed in terms of a notion of bracketing entropy adapted to martingale settings.

Designing reward functions for reinforcement learning is difficult: besides specifying which behavior is rewarded for a task, the reward also has to discourage undesired outcomes. Misspecified reward functions can lead to unintended negative side effects, and overall unsafe behavior. To overcome this problem, recent work proposed to augment the specified reward function with an impact regularizer that discourages behavior that has a big impact on the environment. Although initial results with impact regularizers seem promising in mitigating some types of side effects, important challenges remain. In this paper, we examine the main current challenges of impact regularizers and relate them to fundamental design decisions. We discuss in detail which challenges recent approaches address and which remain unsolved. Finally, we explore promising directions to overcome the unsolved challenges in preventing negative side effects with impact regularizers.

Navigation problems under unknown varying conditions are among the most important and well-studied problems in the control field. Classic model-based adaptive control methods can be applied only when a convenient model of the plant or environment is provided. Recent model-free adaptive control methods aim at removing this dependency by learning the physical characteristics of the plant and/or process directly from sensor feedback. Although there have been prior attempts at improving these techniques, it remains an open question as to whether it is possible to cope with real-world uncertainties in a control system that is fully based on either paradigm. We propose a conceptually simple learning-based approach composed of a full state feedback controller, tuned robustly by a deep reinforcement learning framework based on the Soft Actor-Critic algorithm. We compare it, in realistic simulations, to a model-free controller that uses the same deep reinforcement learning framework for the control of a micro aerial vehicle under wind gust. The results indicate the great potential of learning-based adaptive control methods in modern dynamical systems.