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Zeyu Jia, Alexander Rakhlin, Ayush Sekhari, Chen-Yu Wei

We revisit the problem of offline reinforcement learning with value function realizability but without Bellman completeness. Previous work by Xie and Jiang (2021) and Foster et al. (2022) left open the question whether a bounded concentrability coefficient along with trajectory-based offline data admits a polynomial sample complexity. In this work, we provide a negative answer to this question for the task of offline policy evaluation. In addition to addressing this question, we provide a rather complete picture for offline policy evaluation with only value function realizability. Our primary findings are threefold: 1) The sample complexity of offline policy evaluation is governed by the concentrability coefficient in an aggregated Markov Transition Model jointly determined by the function class and the offline data distribution, rather than that in the original MDP. This unifies and generalizes the ideas of Xie and Jiang (2021) and Foster et al. (2022), 2) The concentrability coefficient in the aggregated Markov Transition Model may grow exponentially with the horizon length, even when the concentrability coefficient in the original MDP is small and the offline data is admissible (i.e., the data distribution equals the occupancy measure of some policy), 3) Under value function realizability, there is a generic reduction that can convert any hard instance with admissible data to a hard instance with trajectory data, implying that trajectory data offers no extra benefits over admissible data. These three pieces jointly resolve the open problem, though each of them could be of independent interest.

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Philip Amortila, Dylan J. Foster, Nan Jiang, Ayush Sekhari, Tengyang Xie

The theories of offline and online reinforcement learning, despite having evolved in parallel, have begun to show signs of the possibility for a unification, with algorithms and analysis techniques for one setting often having natural counterparts in the other. However, the notion of density ratio modeling, an emerging paradigm in offline RL, has been largely absent from online RL, perhaps for good reason: the very existence and boundedness of density ratios relies on access to an exploratory dataset with good coverage, but the core challenge in online RL is to collect such a dataset without having one to start. In this work we show -- perhaps surprisingly -- that density ratio-based algorithms have online counterparts. Assuming only the existence of an exploratory distribution with good coverage, a structural condition known as coverability (Xie et al., 2023), we give a new algorithm (GLOW) that uses density ratio realizability and value function realizability to perform sample-efficient online exploration. GLOW addresses unbounded density ratios via careful use of truncation, and combines this with optimism to guide exploration. GLOW is computationally inefficient; we complement it with a more efficient counterpart, HyGLOW, for the Hybrid RL setting (Song et al., 2022) wherein online RL is augmented with additional offline data. HyGLOW is derived as a special case of a more general meta-algorithm that provides a provable black-box reduction from hybrid RL to offline RL, which may be of independent interest.

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Yifei Zhou, Ayush Sekhari, Yuda Song, Wen Sun

Hybrid RL is the setting where an RL agent has access to both offline data and online data by interacting with the real-world environment. In this work, we propose a new hybrid RL algorithm that combines an on-policy actor-critic method with offline data. On-policy methods such as policy gradient and natural policy gradient (NPG) have shown to be more robust to model misspecification, though sometimes it may not be as sample efficient as methods that rely on off-policy learning. On the other hand, offline methods that depend on off-policy training often require strong assumptions in theory and are less stable to train in practice. Our new approach integrates a procedure of off-policy training on the offline data into an on-policy NPG framework. We show that our approach, in theory, can obtain a best-of-both-worlds type of result -- it achieves the state-of-art theoretical guarantees of offline RL when offline RL-specific assumptions hold, while at the same time maintaining the theoretical guarantees of on-policy NPG regardless of the offline RL assumptions' validity. Experimentally, in challenging rich-observation environments, we show that our approach outperforms a state-of-the-art hybrid RL baseline which only relies on off-policy policy optimization, demonstrating the empirical benefit of combining on-policy and off-policy learning. Our code is publicly available at https://github.com/YifeiZhou02/HNPG.

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Zeyu Jia, Gene Li, Alexander Rakhlin, Ayush Sekhari, Nathan Srebro

We study the problem of agnostic PAC reinforcement learning (RL): given a policy class $\Pi$, how many rounds of interaction with an unknown MDP (with a potentially large state and action space) are required to learn an $\epsilon$-suboptimal policy with respect to $\Pi$? Towards that end, we introduce a new complexity measure, called the \emph{spanning capacity}, that depends solely on the set $\Pi$ and is independent of the MDP dynamics. With a generative model, we show that for any policy class $\Pi$, bounded spanning capacity characterizes PAC learnability. However, for online RL, the situation is more subtle. We show there exists a policy class $\Pi$ with a bounded spanning capacity that requires a superpolynomial number of samples to learn. This reveals a surprising separation for agnostic learnability between generative access and online access models (as well as between deterministic/stochastic MDPs under online access). On the positive side, we identify an additional \emph{sunflower} structure, which in conjunction with bounded spanning capacity enables statistically efficient online RL via a new algorithm called POPLER, which takes inspiration from classical importance sampling methods as well as techniques for reachable-state identification and policy evaluation in reward-free exploration.

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Ayush Sekhari, Karthik Sridharan, Wen Sun, Runzhe Wu

We consider the problem of contextual bandits and imitation learning, where the learner lacks direct knowledge of the executed action's reward. Instead, the learner can actively query an expert at each round to compare two actions and receive noisy preference feedback. The learner's objective is two-fold: to minimize the regret associated with the executed actions, while simultaneously, minimizing the number of comparison queries made to the expert. In this paper, we assume that the learner has access to a function class that can represent the expert's preference model under appropriate link functions, and provide an algorithm that leverages an online regression oracle with respect to this function class for choosing its actions and deciding when to query. For the contextual bandit setting, our algorithm achieves a regret bound that combines the best of both worlds, scaling as $O(\min\{\sqrt{T}, d/\Delta\})$, where $T$ represents the number of interactions, $d$ represents the eluder dimension of the function class, and $\Delta$ represents the minimum preference of the optimal action over any suboptimal action under all contexts. Our algorithm does not require the knowledge of $\Delta$, and the obtained regret bound is comparable to what can be achieved in the standard contextual bandits setting where the learner observes reward signals at each round. Additionally, our algorithm makes only $O(\min\{T, d^2/\Delta^2\})$ queries to the expert. We then extend our algorithm to the imitation learning setting, where the learning agent engages with an unknown environment in episodes of length $H$ each, and provide similar guarantees for regret and query complexity. Interestingly, our algorithm for imitation learning can even learn to outperform the underlying expert, when it is suboptimal, highlighting a practical benefit of preference-based feedback in imitation learning.

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Ayush Sekhari, Karthik Sridharan, Wen Sun, Runzhe Wu

We consider the problem of Imitation Learning (IL) by actively querying noisy expert for feedback. While imitation learning has been empirically successful, much of prior work assumes access to noiseless expert feedback which is not practical in many applications. In fact, when one only has access to noisy expert feedback, algorithms that rely on purely offline data (non-interactive IL) can be shown to need a prohibitively large number of samples to be successful. In contrast, in this work, we provide an interactive algorithm for IL that uses selective sampling to actively query the noisy expert for feedback. Our contributions are twofold: First, we provide a new selective sampling algorithm that works with general function classes and multiple actions, and obtains the best-known bounds for the regret and the number of queries. Next, we extend this analysis to the problem of IL with noisy expert feedback and provide a new IL algorithm that makes limited queries. Our algorithm for selective sampling leverages function approximation, and relies on an online regression oracle w.r.t.~the given model class to predict actions, and to decide whether to query the expert for its label. On the theoretical side, the regret bound of our algorithm is upper bounded by the regret of the online regression oracle, while the query complexity additionally depends on the eluder dimension of the model class. We complement this with a lower bound that demonstrates that our results are tight. We extend our selective sampling algorithm for IL with general function approximation and provide bounds on both the regret and the number of queries made to the noisy expert. A key novelty here is that our regret and query complexity bounds only depend on the number of times the optimal policy (and not the noisy expert, or the learner) go to states that have a small margin.

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Badih Ghazi, Pritish Kamath, Ravi Kumar, Pasin Manurangsi, Ayush Sekhari, Chiyuan Zhang

We consider the learning--unlearning paradigm defined as follows. First given a dataset, the goal is to learn a good predictor, such as one minimizing a certain loss. Subsequently, given any subset of examples that wish to be unlearnt, the goal is to learn, without the knowledge of the original training dataset, a good predictor that is identical to the predictor that would have been produced when learning from scratch on the surviving examples. We propose a new ticketed model for learning--unlearning wherein the learning algorithm can send back additional information in the form of a small-sized (encrypted) ``ticket'' to each participating training example, in addition to retaining a small amount of ``central'' information for later. Subsequently, the examples that wish to be unlearnt present their tickets to the unlearning algorithm, which additionally uses the central information to return a new predictor. We provide space-efficient ticketed learning--unlearning schemes for a broad family of concept classes, including thresholds, parities, intersection-closed classes, among others. En route, we introduce the count-to-zero problem, where during unlearning, the goal is to simply know if there are any examples that survived. We give a ticketed learning--unlearning scheme for this problem that relies on the construction of Sperner families with certain properties, which might be of independent interest.

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Jimmy Z. Di, Jack Douglas, Jayadev Acharya, Gautam Kamath, Ayush Sekhari

We introduce camouflaged data poisoning attacks, a new attack vector that arises in the context of machine unlearning and other settings when model retraining may be induced. An adversary first adds a few carefully crafted points to the training dataset such that the impact on the model's predictions is minimal. The adversary subsequently triggers a request to remove a subset of the introduced points at which point the attack is unleashed and the model's predictions are negatively affected. In particular, we consider clean-label targeted attacks (in which the goal is to cause the model to misclassify a specific test point) on datasets including CIFAR-10, Imagenette, and Imagewoof. This attack is realized by constructing camouflage datapoints that mask the effect of a poisoned dataset.

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Dylan J. Foster, Noah Golowich, Jian Qian, Alexander Rakhlin, Ayush Sekhari

We consider the problem of interactive decision making, encompassing structured bandits and reinforcement learning with general function approximation. Recently, Foster et al. (2021) introduced the Decision-Estimation Coefficient, a measure of statistical complexity that lower bounds the optimal regret for interactive decision making, as well as a meta-algorithm, Estimation-to-Decisions, which achieves upper bounds in terms of the same quantity. Estimation-to-Decisions is a reduction, which lifts algorithms for (supervised) online estimation into algorithms for decision making. In this note, we show that by combining Estimation-to-Decisions with a specialized form of optimistic estimation introduced by Zhang (2022), it is possible to obtain guarantees that improve upon those of Foster et al. (2021) by accommodating more lenient notions of estimation error. We use this approach to derive regret bounds for model-free reinforcement learning with value function approximation.

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Yuda Song, Yifei Zhou, Ayush Sekhari, J. Andrew Bagnell, Akshay Krishnamurthy, Wen Sun

We consider a hybrid reinforcement learning setting (Hybrid RL), in which an agent has access to an offline dataset and the ability to collect experience via real-world online interaction. The framework mitigates the challenges that arise in both pure offline and online RL settings, allowing for the design of simple and highly effective algorithms, in both theory and practice. We demonstrate these advantages by adapting the classical Q learning/iteration algorithm to the hybrid setting, which we call Hybrid Q-Learning or Hy-Q. In our theoretical results, we prove that the algorithm is both computationally and statistically efficient whenever the offline dataset supports a high-quality policy and the environment has bounded bilinear rank. Notably, we require no assumptions on the coverage provided by the initial distribution, in contrast with guarantees for policy gradient/iteration methods. In our experimental results, we show that Hy-Q with neural network function approximation outperforms state-of-the-art online, offline, and hybrid RL baselines on challenging benchmarks, including Montezuma's Revenge.

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