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  1. Chaudhuri, Kamalika and (Ed.)
    We study the problem of reinforcement learning (RL) with low (policy) switching cost {—} a problem well-motivated by real-life RL applications in which deployments of new policies are costly and the number of policy updates must be low. In this paper, we propose a new algorithm based on stage-wise exploration and adaptive policy elimination that achieves a regret of $\widetilde{O}(\sqrt{H^4S^2AT})$ while requiring a switching cost of $O(HSA \log\log T)$. This is an exponential improvement over the best-known switching cost $O(H^2SA\log T)$ among existing methods with $\widetilde{O}(\mathrm{poly}(H,S,A)\sqrt{T})$ regret. In the above, $S,A$ denotes the number of states and actions in anmore »$H$-horizon episodic Markov Decision Process model with unknown transitions, and $T$ is the number of steps. As a byproduct of our new techniques, we also derive a reward-free exploration algorithm with a switching cost of $O(HSA)$. Furthermore, we prove a pair of information-theoretical lower bounds which say that (1) Any no-regret algorithm must have a switching cost of $\Omega(HSA)$; (2) Any $\widetilde{O}(\sqrt{T})$ regret algorithm must incur a switching cost of $\Omega(HSA\log\log T)$. Both our algorithms are thus optimal in their switching costs.« less
    Free, publicly-accessible full text available June 1, 2023
  2. Goal-oriented Reinforcement Learning, where the agent needs to reach the goal state while simultaneously minimizing the cost, has received significant attention in real-world applications. Its theoretical formulation, stochastic shortest path (SSP), has been intensively researched in the online setting. Nevertheless, it remains understudied when such an online interaction is prohibited and only historical data is provided. In this paper, we consider the offline stochastic shortest path problem when the state space and the action space are finite. We design the simple value iteration-based algorithms for tackling both offline policy evaluation (OPE) and offline policy learning tasks. Notably, our analysis ofmore »these simple algorithms yields strong instance-dependent bounds which can imply worst-case bounds that are near-minimax optimal. We hope our study could help illuminate the fundamental statistical limits of the offline SSP problem and motivate further studies beyond the scope of current consideration.« less
    Free, publicly-accessible full text available May 1, 2023
  3. Offline reinforcement learning, which seeks to utilize offline/historical data to optimize sequential decision-making strategies, has gained surging prominence in recent studies. Due to the advantage that appropriate function approximators can help mitigate the sample complexity burden in modern reinforcement learning problems, existing endeavors usually enforce powerful function representation models (e.g. neural networks) to learn the optimal policies. However, a precise understanding of the statistical limits with function representations, remains elusive, even when such a representation is linear. Towards this goal, we study the statistical limits of offline reinforcement learning with linear model representations. To derive the tight offline learning bound,more »we design the variance-aware pessimistic value iteration (VAPVI), which adopts the conditional variance information of the value function for time-inhomogeneous episodic linear Markov decision processes (MDPs). VAPVI leverages estimated variances of the value functions to reweight the Bellman residuals in the least-square pessimistic value iteration and provides improved offline learning bounds over the best-known existing results (whereas the Bellman residuals are equally weighted by design). More importantly, our learning bounds are expressed in terms of system quantities, which provide natural instance-dependent characterizations that previous results are short of. We hope our results draw a clearer picture of what offline learning should look like when linear representations are provided.« less
    Free, publicly-accessible full text available April 1, 2023
  4. We consider how to privately share the personalized privacy losses incurred by objective perturbation, using per-instance differential privacy (pDP). Standard differential privacy (DP) gives us a worst-case bound that might be orders of magnitude larger than the privacy loss to a particular individual relative to a fixed dataset. The pDP framework provides a more fine-grained analysis of the privacy guarantee to a target individual, but the per-instance privacy loss itself might be a function of sensitive data. In this paper, we analyze the per-instance privacy loss of releasing a private empirical risk minimizer learned via objective perturbation, and propose amore »group of methods to privately and accurately publish the pDP losses at little to no additional privacy cost.« less
    Free, publicly-accessible full text available December 1, 2022
  5. We study the \emph{offline reinforcement learning} (offline RL) problem, where the goal is to learn a reward-maximizing policy in an unknown \emph{Markov Decision Process} (MDP) using the data coming from a policy $\mu$. In particular, we consider the sample complexity problems of offline RL for the finite horizon MDPs. Prior works derive the information-theoretical lower bounds based on different data-coverage assumptions and their upper bounds are expressed by the covering coefficients which lack the explicit characterization of system quantities. In this work, we analyze the \emph{Adaptive Pessimistic Value Iteration} (APVI) algorithm and derive the suboptimality upper bound that nearly matchesmore »$ O\left(\sum_{h=1}^H\sum_{s_h,a_h}d^{\pi^\star}_h(s_h,a_h)\sqrt{\frac{\mathrm{Var}_{P_{s_h,a_h}}{(V^\star_{h+1}+r_h)}}{d^\mu_h(s_h,a_h)}}\sqrt{\frac{1}{n}}\right). $ We also prove an information-theoretical lower bound to show this quantity is required under the weak assumption that $d^\mu_h(s_h,a_h)>0$ if $d^{\pi^\star}_h(s_h,a_h)>0$. Here $\pi^\star$ is a optimal policy, $\mu$ is the behavior policy and $d(s_h,a_h)$ is the marginal state-action probability. We call this adaptive bound the \emph{intrinsic offline reinforcement learning bound} since it directly implies all the existing optimal results: minimax rate under uniform data-coverage assumption, horizon-free setting, single policy concentrability, and the tight problem-dependent results. Later, we extend the result to the \emph{assumption-free} regime (where we make no assumption on $ \mu$) and obtain the assumption-free intrinsic bound. Due to its generic form, we believe the intrinsic bound could help illuminate what makes a specific problem hard and reveal the fundamental challenges in offline RL.« less
    Free, publicly-accessible full text available December 1, 2022
  6. We consider the problem of offline reinforcement learning (RL) -- a well-motivated setting of RL that aims at policy optimization using only historical data. Despite its wide applicability, theoretical understandings of offline RL, such as its optimal sample complexity, remain largely open even in basic settings such as \emph{tabular} Markov Decision Processes (MDPs). In this paper, we propose Off-Policy Double Variance Reduction (OPDVR), a new variance reduction based algorithm for offline RL. Our main result shows that OPDVR provably identifies an ϵ-optimal policy with O˜(H2/dmϵ2) episodes of offline data in the finite-horizon stationary transition setting, where H is the horizonmore »length and dm is the minimal marginal state-action distribution induced by the behavior policy. This improves over the best known upper bound by a factor of H. Moreover, we establish an information-theoretic lower bound of Ω(H2/dmϵ2) which certifies that OPDVR is optimal up to logarithmic factors. Lastly, we show that OPDVR also achieves rate-optimal sample complexity under alternative settings such as the finite-horizon MDPs with non-stationary transitions and the infinite horizon MDPs with discounted rewards.« less
    Free, publicly-accessible full text available December 1, 2022
  7. Krause, Andreas (Ed.)
    The Private Aggregation of Teacher Ensembles (PATE) framework is one of the most promising recent approaches in differentially private learning. Existing theoretical analysis shows that PATE consistently learns any VC-classes in the realizable setting, but falls short in explaining its success in more general cases where the error rate of the optimal classifier is bounded away from zero. We fill in this gap by introducing the Tsybakov Noise Condition (TNC) and establish stronger and more interpretable learning bounds. These bounds provide new insights into when PATE works and improve over existing results even in the narrower realizable setting. We alsomore »investigate the compelling idea of using active learning for saving privacy budget, and empirical studies show the effectiveness of this new idea. The novel components in the proofs include a more refined analysis of the majority voting classifier — which could be of independent interest — and an observation that the synthetic “student” learning problem is nearly realizable by construction under the Tsybakov noise condition.« less
    Free, publicly-accessible full text available November 22, 2022
  8. This work studies the statistical limits of uniform convergence for offline policy evaluation (OPE) problems with model-based methods (for episodic MDP) and provides a unified framework towards optimal learning for several well-motivated offline tasks. Uniform OPE supΠ|Qπ−Q̂ π|<ϵ is a stronger measure than the point-wise OPE and ensures offline learning when Π contains all policies (the global class). In this paper, we establish an Ω(H2S/dmϵ2) lower bound (over model-based family) for the global uniform OPE and our main result establishes an upper bound of Õ (H2/dmϵ2) for the \emph{local} uniform convergence that applies to all \emph{near-empirically optimal} policies for themore »MDPs with \emph{stationary} transition. Here dm is the minimal marginal state-action probability. Critically, the highlight in achieving the optimal rate Õ (H2/dmϵ2) is our design of \emph{singleton absorbing MDP}, which is a new sharp analysis tool that works with the model-based approach. We generalize such a model-based framework to the new settings: offline task-agnostic and the offline reward-free with optimal complexity Õ (H2log(K)/dmϵ2) (K is the number of tasks) and Õ (H2S/dmϵ2) respectively. These results provide a unified solution for simultaneously solving different offline RL problems.« less
    Free, publicly-accessible full text available October 1, 2022
  9. Free, publicly-accessible full text available August 15, 2022
  10. COVID-19 pandemic has an unprecedented impact all over the world since early 2020. During this public health crisis, reliable forecasting of the disease becomes critical for resource allocation and administrative planning. The results from compartmental models such as SIR and SEIR are popularly referred by CDC and news media. With more and more COVID-19 data becoming available, we examine the following question: Can a direct data-driven approach without modeling the disease spreading dynamics outperform the well referred compartmental models and their variants? In this paper, we show the possibility. It is observed that as COVID-19 spreads at different speed andmore »scale in different geographic regions, it is highly likely that similar progression patterns are shared among these regions within different time periods. This intuition lead us to develop a new neural forecasting model, called Attention Crossing Time Series (ACTS), that makes forecasts via comparing patterns across time series obtained from multiple regions. The attention mechanism originally developed for natural language processing can be leveraged and generalized to materialize this idea. Among 13 out of 18 testings including forecasting newly con rmed cases, hospitalizations and deaths, ACTS outperforms all the leading COVID-19 forecasters highlighted by CDC.« less