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.

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.

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.

Learning by interacting with an environment, in the standard online reinforcement learning (RL) protocol, has led to impressive results across a number of domains. State-of-the-art RL algorithms are quite general, employing function approximation to scale to complex environments with minimal domain expertise and inductive bias. However, online RL agents are also notoriously sample inefficient, often requiring billions of environment interactions to achieve suitable performance. This issue is particularly salient when the environment requires sophisticated exploration and a high quality reset distribution is unavailable to help overcome the exploration challenge. As a consequence, the practical success of online RL and related policy gradient/improvement methods has been largely restricted to settings where a high quality simulator is available. To overcome the issue of sample inefficiency, attention has turned to the offline RL setting [Levine et al., 2020], where, rather than interacting with the environment, the agent trains on a large dataset of experience collected in some other manner (e.g., by a system running in production or an expert). While these methods still require a large dataset, they mitigate the sample complexity concerns of online RL, since the dataset can be collected without compromising system performance. However, offline RL methods can suffer from distribution shift, where the state distribution induced by the learned policy differs significantly from the offline distribution [Wang et al., 2021]. Existing provable approaches for addressing distribution shift are computationally intractable, while empirical approaches rely on heuristics that can be sensitive to the domain and offline dataset (as we will see).

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.

A central problem in online learning and decision making -- from bandits to reinforcement learning -- is to understand what modeling assumptions lead to sample-efficient learning guarantees. We consider a general adversarial decision making framework that encompasses (structured) bandit problems with adversarial rewards and reinforcement learning problems with adversarial dynamics. Our main result is to show -- via new upper and lower bounds -- that the Decision-Estimation Coefficient, a complexity measure introduced by Foster et al. in the stochastic counterpart to our setting, is necessary and sufficient to obtain low regret for adversarial decision making. However, compared to the stochastic setting, one must apply the Decision-Estimation Coefficient to the convex hull of the class of models (or, hypotheses) under consideration. This establishes that the price of accommodating adversarial rewards or dynamics is governed by the behavior of the model class under convexification, and recovers a number of existing results -- both positive and negative. En route to obtaining these guarantees, we provide new structural results that connect the Decision-Estimation Coefficient to variants of other well-known complexity measures, including the Information Ratio of Russo and Van Roy and the Exploration-by-Optimization objective of Lattimore and Gy\"{o}rgy.

We study reinforcement learning with function approximation for large-scale Partially Observable Markov Decision Processes (POMDPs) where the state space and observation space are large or even continuous. Particularly, we consider Hilbert space embeddings of POMDP where the feature of latent states and the feature of observations admit a conditional Hilbert space embedding of the observation emission process, and the latent state transition is deterministic. Under the function approximation setup where the optimal latent state-action $Q$-function is linear in the state feature, and the optimal $Q$-function has a gap in actions, we provide a \emph{computationally and statistically efficient} algorithm for finding the \emph{exact optimal} policy. We show our algorithm's computational and statistical complexities scale polynomially with respect to the horizon and the intrinsic dimension of the feature on the observation space. Furthermore, we show both the deterministic latent transitions and gap assumptions are necessary to avoid statistical complexity exponential in horizon or dimension. Since our guarantee does not have an explicit dependence on the size of the state and observation spaces, our algorithm provably scales to large-scale POMDPs.

We study Reinforcement Learning for partially observable dynamical systems using function approximation. We propose a new \textit{Partially Observable Bilinear Actor-Critic framework}, that is general enough to include models such as observable tabular Partially Observable Markov Decision Processes (POMDPs), observable Linear-Quadratic-Gaussian (LQG), Predictive State Representations (PSRs), as well as a newly introduced model Hilbert Space Embeddings of POMDPs and observable POMDPs with latent low-rank transition. Under this framework, we propose an actor-critic style algorithm that is capable of performing agnostic policy learning. Given a policy class that consists of memory based policies (that look at a fixed-length window of recent observations), and a value function class that consists of functions taking both memory and future observations as inputs, our algorithm learns to compete against the best memory-based policy in the given policy class. For certain examples such as undercomplete observable tabular POMDPs, observable LQGs and observable POMDPs with latent low-rank transition, by implicitly leveraging their special properties, our algorithm is even capable of competing against the globally optimal policy without paying an exponential dependence on the horizon in its sample complexity.

Multi-epoch, small-batch, Stochastic Gradient Descent (SGD) has been the method of choice for learning with large over-parameterized models. A popular theory for explaining why SGD works well in practice is that the algorithm has an implicit regularization that biases its output towards a good solution. Perhaps the theoretically most well understood learning setting for SGD is that of Stochastic Convex Optimization (SCO), where it is well known that SGD learns at a rate of $O(1/\sqrt{n})$, where $n$ is the number of samples. In this paper, we consider the problem of SCO and explore the role of implicit regularization, batch size and multiple epochs for SGD. Our main contributions are threefold: (a) We show that for any regularizer, there is an SCO problem for which Regularized Empirical Risk Minimzation fails to learn. This automatically rules out any implicit regularization based explanation for the success of SGD. (b) We provide a separation between SGD and learning via Gradient Descent on empirical loss (GD) in terms of sample complexity. We show that there is an SCO problem such that GD with any step size and number of iterations can only learn at a suboptimal rate: at least $\widetilde{\Omega}(1/n^{5/12})$. (c) We present a multi-epoch variant of SGD commonly used in practice. We prove that this algorithm is at least as good as single pass SGD in the worst case. However, for certain SCO problems, taking multiple passes over the dataset can significantly outperform single pass SGD. We extend our results to the general learning setting by showing a problem which is learnable for any data distribution, and for this problem, SGD is strictly better than RERM for any regularization function. We conclude by discussing the implications of our results for deep learning, and show a separation between SGD and ERM for two layer diagonal neural networks.

Reinforcement Learning (RL) has achieved several remarkable empirical successes in the last decade, which include playing Atari 2600 video games at superhuman levels (Mnih et al., 2015), AlphaGo or AlphaGo Zero surpassing champions in Go (Silver et al., 2018), AlphaStar's victory over top-ranked professional players in StarCraft (Vinyals et al., 2019), or practical self-driving cars. These applications all correspond to the setting of rich observations, where the state space is very large and where observations may be images, text or audio data. In contrast, most provably efficient RL algorithms are still limited to the classical tabular setting where the state space is small (Kearns and Singh, 2002; Brafman and Tennenholtz, 2002; Azar et al., 2017; Dann et al., 2019) and do not scale to the rich observation setting. To derive guarantees for large state spaces, much of the existing work in RL theory relies on a realizability and a low-rank assumption (Krishnamurthy et al., 2016; Jiang et al., 2017; Dann et al., 2018; Du et al., 2019a; Misra et al., 2020; Agarwal et al., 2020b). Different notions of rank have been adopted in the literature, including that of a low-rank transition matrix (Jin et al., 2020a), a low Bellman rank (Jiang et al., 2017), Wittness rank (Sun et al., 2019), Eluder dimension (Osband and Van Roy, 2014), Bellman-Eluder dimension (Jin et al., 2021), or bilinear classes (Du et al., 2021).