ASID: Active Exploration for System Identification in Robotic Manipulation

Model-free control strategies such as reinforcement learning have shown the ability to learn control strategies without requiring an accurate model or simulator of the world. While this is appealing due to the lack of modeling requirements, such methods can be sample inefficient, making them impractical in many real-world domains. On the other hand, model-based control techniques leveraging accurate simulators can circumvent these challenges and use a large amount of cheap simulation data to learn controllers that can effectively transfer to the real world. The challenge with such model-based techniques is the requirement for an extremely accurate simulation, requiring both the specification of appropriate simulation assets and physical parameters. This requires considerable human effort to design for every environment being considered. In this work, we propose a learning system that can leverage a small amount of real-world data to autonomously refine a simulation model and then plan an accurate control strategy that can be deployed in the real world. Our approach critically relies on utilizing an initial (possibly inaccurate) simulator to design effective exploration policies that, when deployed in the real world, collect high-quality data. We demonstrate the efficacy of this paradigm in identifying articulation, mass, and other physical parameters in several challenging robotic manipulation tasks, and illustrate that only a small amount of real-world data can allow for effective sim-to-real transfer. Project website at https://weirdlabuw.github.io/asid

Fair Active Learning in Low-Data Regimes

In critical machine learning applications, ensuring fairness is essential to avoid perpetuating social inequities. In this work, we address the challenges of reducing bias and improving accuracy in data-scarce environments, where the cost of collecting labeled data prohibits the use of large, labeled datasets. In such settings, active learning promises to maximize marginal accuracy gains of small amounts of labeled data. However, existing applications of active learning for fairness fail to deliver on this, typically requiring large labeled datasets, or failing to ensure the desired fairness tolerance is met on the population distribution. To address such limitations, we introduce an innovative active learning framework that combines an exploration procedure inspired by posterior sampling with a fair classification subroutine. We demonstrate that this framework performs effectively in very data-scarce regimes, maximizing accuracy while satisfying fairness constraints with high probability. We evaluate our proposed approach using well-established real-world benchmark datasets and compare it against state-of-the-art methods, demonstrating its effectiveness in producing fair models, and improvement over existing methods.

Optimal Exploration for Model-Based RL in Nonlinear Systems

Learning to control unknown nonlinear dynamical systems is a fundamental problem in reinforcement learning and control theory. A commonly applied approach is to first explore the environment (exploration), learn an accurate model of it (system identification), and then compute an optimal controller with the minimum cost on this estimated system (policy optimization). While existing work has shown that it is possible to learn a uniformly good model of the system~\citep{mania2020active}, in practice, if we aim to learn a good controller with a low cost on the actual system, certain system parameters may be significantly more critical than others, and we therefore ought to focus our exploration on learning such parameters. In this work, we consider the setting of nonlinear dynamical systems and seek to formally quantify, in such settings, (a) which parameters are most relevant to learning a good controller, and (b) how we can best explore so as to minimize uncertainty in such parameters. Inspired by recent work in linear systems~\citep{wagenmaker2021task}, we show that minimizing the controller loss in nonlinear systems translates to estimating the system parameters in a particular, task-dependent metric. Motivated by this, we develop an algorithm able to efficiently explore the system to reduce uncertainty in this metric, and prove a lower bound showing that our approach learns a controller at a near-instance-optimal rate. Our algorithm relies on a general reduction from policy optimization to optimal experiment design in arbitrary systems, and may be of independent interest. We conclude with experiments demonstrating the effectiveness of our method in realistic nonlinear robotic systems.

Instance-Optimality in Interactive Decision Making: Toward a Non-Asymptotic Theory

We consider the development of adaptive, instance-dependent algorithms for interactive decision making (bandits, reinforcement learning, and beyond) that, rather than only performing well in the worst case, adapt to favorable properties of real-world instances for improved performance. We aim for instance-optimality, a strong notion of adaptivity which asserts that, on any particular problem instance, the algorithm under consideration outperforms all consistent algorithms. Instance-optimality enjoys a rich asymptotic theory originating from the work of \citet{lai1985asymptotically,graves1997asymptotically}, but non-asymptotic guarantees have remained elusive outside of certain special cases. Even for problems as simple as tabular reinforcement learning, existing algorithms do not attain instance-optimal performance until the number of rounds of interaction is doubly exponential in the number of states. In this paper, we take the first step toward developing a non-asymptotic theory of instance-optimal decision making with general function approximation. We introduce a new complexity measure, the Allocation-Estimation Coefficient (AEC), and provide a new algorithm, $\mathsf{AE}^2$, which attains non-asymptotic instance-optimal performance at a rate controlled by the AEC. Our results recover the best known guarantees for well-studied problems such as finite-armed and linear bandits and, when specialized to tabular reinforcement learning, attain the first instance-optimal regret bounds with polynomial dependence on all problem parameters, improving over prior work exponentially. We complement these results with lower bounds that show that i) existing notions of statistical complexity are insufficient to derive non-asymptotic guarantees, and ii) under certain technical conditions, boundedness of the AEC is necessary to learn an instance-optimal allocation of decisions in finite time.

Leveraging Offline Data in Online Reinforcement Learning

Two central paradigms have emerged in the reinforcement learning (RL) community: online RL and offline RL. In the online RL setting, the agent has no prior knowledge of the environment, and must interact with it in order to find an $\epsilon$-optimal policy. In the offline RL setting, the learner instead has access to a fixed dataset to learn from, but is unable to otherwise interact with the environment, and must obtain the best policy it can from this offline data. Practical scenarios often motivate an intermediate setting: if we have some set of offline data and, in addition, may also interact with the environment, how can we best use the offline data to minimize the number of online interactions necessary to learn an $\epsilon$-optimal policy? In this work, we consider this setting, which we call the \textsf{FineTuneRL} setting, for MDPs with linear structure. We characterize the necessary number of online samples needed in this setting given access to some offline dataset, and develop an algorithm, \textsc{FTPedel}, which is provably optimal. We show through an explicit example that combining offline data with online interactions can lead to a provable improvement over either purely offline or purely online RL. Finally, our results illustrate the distinction between \emph{verifiable} learning, the typical setting considered in online RL, and \emph{unverifiable} learning, the setting often considered in offline RL, and show that there is a formal separation between these regimes.

Instance-Dependent Near-Optimal Policy Identification in Linear MDPs via Online Experiment Design

While much progress has been made in understanding the minimax sample complexity of reinforcement learning (RL) -- the complexity of learning on the "worst-case" instance -- such measures of complexity often do not capture the true difficulty of learning. In practice, on an "easy" instance, we might hope to achieve a complexity far better than that achievable on the worst-case instance. In this work we seek to understand the "instance-dependent" complexity of learning near-optimal policies (PAC RL) in the setting of RL with linear function approximation. We propose an algorithm, \textsc{Pedel}, which achieves a fine-grained instance-dependent measure of complexity, the first of its kind in the RL with function approximation setting, thereby capturing the difficulty of learning on each particular problem instance. Through an explicit example, we show that \textsc{Pedel} yields provable gains over low-regret, minimax-optimal algorithms and that such algorithms are unable to hit the instance-optimal rate. Our approach relies on a novel online experiment design-based procedure which focuses the exploration budget on the "directions" most relevant to learning a near-optimal policy, and may be of independent interest.

Active Learning with Safety Constraints

Active learning methods have shown great promise in reducing the number of samples necessary for learning. As automated learning systems are adopted into real-time, real-world decision-making pipelines, it is increasingly important that such algorithms are designed with safety in mind. In this work we investigate the complexity of learning the best safe decision in interactive environments. We reduce this problem to a constrained linear bandits problem, where our goal is to find the best arm satisfying certain (unknown) safety constraints. We propose an adaptive experimental design-based algorithm, which we show efficiently trades off between the difficulty of showing an arm is unsafe vs suboptimal. To our knowledge, our results are the first on best-arm identification in linear bandits with safety constraints. In practice, we demonstrate that this approach performs well on synthetic and real world datasets.

Reward-Free RL is No Harder Than Reward-Aware RL in Linear Markov Decision Processes

Reward-free reinforcement learning (RL) considers the setting where the agent does not have access to a reward function during exploration, but must propose a near-optimal policy for an arbitrary reward function revealed only after exploring. In the the tabular setting, it is well known that this is a more difficult problem than PAC RL -- where the agent has access to the reward function during exploration -- with optimal sample complexities in the two settings differing by a factor of $|\mathcal{S}|$, the size of the state space. We show that this separation does not exist in the setting of linear MDPs. We first develop a computationally efficient algorithm for reward-free RL in a $d$-dimensional linear MDP with sample complexity scaling as $\mathcal{O}(d^2/\epsilon^2)$. We then show a matching lower bound of $\Omega(d^2/\epsilon^2)$ on PAC RL. To our knowledge, our approach is the first computationally efficient algorithm to achieve optimal $d$ dependence in linear MDPs, even in the single-reward PAC setting. Our algorithm relies on a novel procedure which efficiently traverses a linear MDP, collecting samples in any given "feature direction", and enjoys a sample complexity scaling optimally in the (linear MDP equivalent of the) maximal state visitation probability. We show that this exploration procedure can also be applied to solve the problem of obtaining "well-conditioned" covariates in linear MDPs.

First-Order Regret in Reinforcement Learning with Linear Function Approximation: A Robust Estimation Approach

Obtaining first-order regret bounds -- regret bounds scaling not as the worst-case but with some measure of the performance of the optimal policy on a given instance -- is a core question in sequential decision-making. While such bounds exist in many settings, they have proven elusive in reinforcement learning with large state spaces. In this work we address this gap, and show that it is possible to obtain regret scaling as $\mathcal{O}(\sqrt{V_1^\star K})$ in reinforcement learning with large state spaces, namely the linear MDP setting. Here $V_1^\star$ is the value of the optimal policy and $K$ is the number of episodes. We demonstrate that existing techniques based on least squares estimation are insufficient to obtain this result, and instead develop a novel robust self-normalized concentration bound based on the robust Catoni mean estimator, which may be of independent interest.

Best Arm Identification with Safety Constraints

The best arm identification problem in the multi-armed bandit setting is an excellent model of many real-world decision-making problems, yet it fails to capture the fact that in the real-world, safety constraints often must be met while learning. In this work we study the question of best-arm identification in safety-critical settings, where the goal of the agent is to find the best safe option out of many, while exploring in a way that guarantees certain, initially unknown safety constraints are met. We first analyze this problem in the setting where the reward and safety constraint takes a linear structure, and show nearly matching upper and lower bounds. We then analyze a much more general version of the problem where we only assume the reward and safety constraint can be modeled by monotonic functions, and propose an algorithm in this setting which is guaranteed to learn safely. We conclude with experimental results demonstrating the effectiveness of our approaches in scenarios such as safely identifying the best drug out of many in order to treat an illness.