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We study reinforcement learning (RL) with linear function approximation. Existing algorithms for this problem only have high-probability regret and/or Probably Approximately Correct (PAC) sample complexity guarantees, which cannot guarantee the convergence to the optimal policy. In this paper, in order to overcome the limitation of existing algorithms, we propose a new algorithm called FLUTE, which enjoys uniform-PAC convergence to the optimal policy with high probability. The uniform-PAC guarantee is the strongest possible guarantee for reinforcement learning in the literature, which can directly imply both PAC and high probability regret bounds, making our algorithm superior to all existing algorithms with linear function approximation. At the core of our algorithm is a novel minimax value function estimator and a multi-level partition scheme to select the training samples from historical observations. Both of these techniques are new and of independent interest.

Online reinforcement learning (RL) algorithms are often difficult to deploy in complex human-facing applications as they may learn slowly and have poor early performance. To address this, we introduce a practical algorithm for incorporating human insight to speed learning. Our algorithm, Constraint Sampling Reinforcement Learning (CSRL), incorporates prior domain knowledge as constraints/restrictions on the RL policy. It takes in multiple potential policy constraints to maintain robustness to misspecification of individual constraints while leveraging helpful ones to learn quickly. Given a base RL learning algorithm (ex. UCRL, DQN, Rainbow) we propose an upper confidence with elimination scheme that leverages the relationship between the constraints, and their observed performance, to adaptively switch among them. We instantiate our algorithm with DQN-type algorithms and UCRL as base algorithms, and evaluate our algorithm in four environments, including three simulators based on real data: recommendations, educational activity sequencing, and HIV treatment sequencing. In all cases, CSRL learns a good policy faster than baselines.

This paper presents a control-theoretic framework which stably combines optimal feedback policies with online learning for control of uncertain nonlinear systems. Given unknown parameters within a bounded range, the resulting adaptive control laws guarantee convergence of the closed-loop system to the state of zero cost. The proposed framework is able to employ the certainty equivalence principle when designing optimal policies and value functions by online adjustment of the learning rate - a mechanism needed to guarantee stable learning and control. The approach is demonstrated on the familiar mountain car problem, where it is shown to yield near-optimal behavior despite the presence of parametric uncertainty.

Let $X$ be a random variable with unknown mean and finite variance. We present a new estimator of the mean of $X$ that is robust with respect to the possible presence of outliers in the sample, provides tight sub-Gaussian deviation guarantees without any additional assumptions on the shape or tails of the distribution, and moreover is asymptotically efficient. This is the first estimator that provably combines all these qualities in one package. Our construction is inspired by robustness properties possessed by the self-normalized sums. Theoretical findings are supplemented by numerical simulations highlighting strong performance of the proposed estimator in comparison with previously known techniques.

Variance estimation is important for statistical inference. It becomes non-trivial when observations are masked by serial dependence structures and time-varying mean structures. Existing methods either ignore or sub-optimally handle these nuisance structures. This paper develops a general framework for the estimation of the long-run variance for time series with non-constant means. The building blocks are difference statistics. The proposed class of estimators is general enough to cover many existing estimators. Necessary and sufficient conditions for consistency are investigated. The first asymptotically optimal estimator is derived. Our proposed estimator is theoretically proven to be invariant to arbitrary mean structures, which may include trends and a possibly divergent number of discontinuities.

A/B testing, or online experiment is a standard business strategy to compare a new product with an old one in pharmaceutical, technological, and traditional industries. Major challenges arise in online experiments of two-sided marketplace platforms (e.g., Uber) where there is only one unit that receives a sequence of treatments over time. In those experiments, the treatment at a given time impacts current outcome as well as future outcomes. The aim of this paper is to introduce a reinforcement learning framework for carrying A/B testing in these experiments, while characterizing the long-term treatment effects. Our proposed testing procedure allows for sequential monitoring and online updating. It is generally applicable to a variety of treatment designs in different industries. In addition, we systematically investigate the theoretical properties (e.g., size and power) of our testing procedure. Finally, we apply our framework to both simulated data and a real-world data example obtained from a technological company to illustrate its advantage over the current practice. A Python implementation of our test is available at //github.com/callmespring/CausalRL.

Multi-arm bandit (MAB) is a classic online learning framework that studies the sequential decision-making in an uncertain environment. The MAB framework, however, overlooks the scenario where the decision-maker cannot take actions (e.g., pulling arms) directly. It is a practically important scenario in many applications such as spectrum sharing, crowdsensing, and edge computing. In these applications, the decision-maker would incentivize other selfish agents to carry out desired actions (i.e., pulling arms on the decision-maker's behalf). This paper establishes the incentivized online learning (IOL) framework for this scenario. The key challenge to design the IOL framework lies in the tight coupling of the unknown environment learning and asymmetric information revelation. To address this, we construct a special Lagrangian function based on which we propose a socially-optimal mechanism for the IOL framework. Our mechanism satisfies various desirable properties such as agent fairness, incentive compatibility, and voluntary participation. It achieves the same asymptotic performance as the state-of-art benchmark that requires extra information. Our analysis also unveils the power of crowd in the IOL framework: a larger agent crowd enables our mechanism to approach more closely the theoretical upper bound of social performance. Numerical results demonstrate the advantages of our mechanism in large-scale edge computing.

The ability to accurately estimate depth information is crucial for many autonomous applications to recognize the surrounded environment and predict the depth of important objects. One of the most recently used techniques is monocular depth estimation where the depth map is inferred from a single image. This paper improves the self-supervised deep learning techniques to perform accurate generalized monocular depth estimation. The main idea is to train the deep model to take into account a sequence of the different frames, each frame is geotagged with its location information. This makes the model able to enhance depth estimation given area semantics. We demonstrate the effectiveness of our model to improve depth estimation results. The model is trained in a realistic environment and the results show improvements in the depth map after adding the location data to the model training phase.

Efficient exploration remains a major challenge for reinforcement learning. One reason is that the variability of the returns often depends on the current state and action, and is therefore heteroscedastic. Classical exploration strategies such as upper confidence bound algorithms and Thompson sampling fail to appropriately account for heteroscedasticity, even in the bandit setting. Motivated by recent findings that address this issue in bandits, we propose to use Information-Directed Sampling (IDS) for exploration in reinforcement learning. As our main contribution, we build on recent advances in distributional reinforcement learning and propose a novel, tractable approximation of IDS for deep Q-learning. The resulting exploration strategy explicitly accounts for both parametric uncertainty and heteroscedastic observation noise. We evaluate our method on Atari games and demonstrate a significant improvement over alternative approaches.

We propose a new method of estimation in topic models, that is not a variation on the existing simplex finding algorithms, and that estimates the number of topics K from the observed data. We derive new finite sample minimax lower bounds for the estimation of A, as well as new upper bounds for our proposed estimator. We describe the scenarios where our estimator is minimax adaptive. Our finite sample analysis is valid for any number of documents (n), individual document length (N_i), dictionary size (p) and number of topics (K), and both p and K are allowed to increase with n, a situation not handled well by previous analyses. We complement our theoretical results with a detailed simulation study. We illustrate that the new algorithm is faster and more accurate than the current ones, although we start out with a computational and theoretical disadvantage of not knowing the correct number of topics K, while we provide the competing methods with the correct value in our simulations.