Inverse Reinforcement Learning from Non-Stationary Learning Agents

In this paper, we study an inverse reinforcement learning problem that involves learning the reward function of a learning agent using trajectory data collected while this agent is learning its optimal policy. To address this problem, we propose an inverse reinforcement learning method that allows us to estimate the policy parameters of the learning agent which can then be used to estimate its reward function. Our method relies on a new variant of the behavior cloning algorithm, which we call bundle behavior cloning, and uses a small number of trajectories generated by the learning agent's policy at different points in time to learn a set of policies that match the distribution of actions observed in the sampled trajectories. We then use the cloned policies to train a neural network model that estimates the reward function of the learning agent. We provide a theoretical analysis to show a complexity result on bound guarantees for our method that beats standard behavior cloning as well as numerical experiments for a reinforcement learning problem that validate the proposed method.

Transfer Reinforcement Learning in Heterogeneous Action Spaces using Subgoal Mapping

In this paper, we consider a transfer reinforcement learning problem involving agents with different action spaces. Specifically, for any new unseen task, the goal is to use a successful demonstration of this task by an expert agent in its action space to enable a learner agent learn an optimal policy in its own different action space with fewer samples than those required if the learner was learning on its own. Existing transfer learning methods across different action spaces either require handcrafted mappings between those action spaces provided by human experts, which can induce bias in the learning procedure, or require the expert agent to share its policy parameters with the learner agent, which does not generalize well to unseen tasks. In this work, we propose a method that learns a subgoal mapping between the expert agent policy and the learner agent policy. Since the expert agent and the learner agent have different action spaces, their optimal policies can have different subgoal trajectories. We learn this subgoal mapping by training a Long Short Term Memory (LSTM) network for a distribution of tasks and then use this mapping to predict the learner subgoal sequence for unseen tasks, thereby improving the speed of learning by biasing the agent's policy towards the predicted learner subgoal sequence. Through numerical experiments, we demonstrate that the proposed learning scheme can effectively find the subgoal mapping underlying the given distribution of tasks. Moreover, letting the learner agent imitate the expert agent's policy with the learnt subgoal mapping can significantly improve the sample efficiency and training time of the learner agent in unseen new tasks.

Distributionally Robust Clustered Federated Learning: A Case Study in Healthcare

In this paper, we address the challenge of heterogeneous data distributions in cross-silo federated learning by introducing a novel algorithm, which we term Cross-silo Robust Clustered Federated Learning (CS-RCFL). Our approach leverages the Wasserstein distance to construct ambiguity sets around each client's empirical distribution that capture possible distribution shifts in the local data, enabling evaluation of worst-case model performance. We then propose a model-agnostic integer fractional program to determine the optimal distributionally robust clustering of clients into coalitions so that possible biases in the local models caused by statistically heterogeneous client datasets are avoided, and analyze our method for linear and logistic regression models. Finally, we discuss a federated learning protocol that ensures the privacy of client distributions, a critical consideration, for instance, when clients are healthcare institutions. We evaluate our algorithm on synthetic and real-world healthcare data.

Perception Stitching: Zero-Shot Perception Encoder Transfer for Visuomotor Robot Policies

Vision-based imitation learning has shown promising capabilities of endowing robots with various motion skills given visual observation. However, current visuomotor policies fail to adapt to drastic changes in their visual observations. We present Perception Stitching that enables strong zero-shot adaptation to large visual changes by directly stitching novel combinations of visual encoders. Our key idea is to enforce modularity of visual encoders by aligning the latent visual features among different visuomotor policies. Our method disentangles the perceptual knowledge with the downstream motion skills and allows the reuse of the visual encoders by directly stitching them to a policy network trained with partially different visual conditions. We evaluate our method in various simulated and real-world manipulation tasks. While baseline methods failed at all attempts, our method could achieve zero-shot success in real-world visuomotor tasks. Our quantitative and qualitative analysis of the learned features of the policy network provides more insights into the high performance of our proposed method.

Risk-averse Learning with Non-Stationary Distributions

Considering non-stationary environments in online optimization enables decision-maker to effectively adapt to changes and improve its performance over time. In such cases, it is favorable to adopt a strategy that minimizes the negative impact of change to avoid potentially risky situations. In this paper, we investigate risk-averse online optimization where the distribution of the random cost changes over time. We minimize risk-averse objective function using the Conditional Value at Risk (CVaR) as risk measure. Due to the difficulty in obtaining the exact CVaR gradient, we employ a zeroth-order optimization approach that queries the cost function values multiple times at each iteration and estimates the CVaR gradient using the sampled values. To facilitate the regret analysis, we use a variation metric based on Wasserstein distance to capture time-varying distributions. Given that the distribution variation is sub-linear in the total number of episodes, we show that our designed learning algorithm achieves sub-linear dynamic regret with high probability for both convex and strongly convex functions. Moreover, theoretical results suggest that increasing the number of samples leads to a reduction in the dynamic regret bounds until the sampling number reaches a specific limit. Finally, we provide numerical experiments of dynamic pricing in a parking lot to illustrate the efficacy of the designed algorithm.

Path Signatures and Graph Neural Networks for Slow Earthquake Analysis: Better Together?

The path signature, having enjoyed recent success in the machine learning community, is a theoretically-driven method for engineering features from irregular paths. On the other hand, graph neural networks (GNN), neural architectures for processing data on graphs, excel on tasks with irregular domains, such as sensor networks. In this paper, we introduce a novel approach, Path Signature Graph Convolutional Neural Networks (PS-GCNN), integrating path signatures into graph convolutional neural networks (GCNN), and leveraging the strengths of both path signatures, for feature extraction, and GCNNs, for handling spatial interactions. We apply our method to analyze slow earthquake sequences, also called slow slip events (SSE), utilizing data from GPS timeseries, with a case study on a GPS sensor network on the east coast of New Zealand's north island. We also establish benchmarks for our method on simulated stochastic differential equations, which model similar reaction-diffusion phenomenon. Our methodology shows promise for future advancement in earthquake prediction and sensor network analysis.

Policy Stitching: Learning Transferable Robot Policies

Training robots with reinforcement learning (RL) typically involves heavy interactions with the environment, and the acquired skills are often sensitive to changes in task environments and robot kinematics. Transfer RL aims to leverage previous knowledge to accelerate learning of new tasks or new body configurations. However, existing methods struggle to generalize to novel robot-task combinations and scale to realistic tasks due to complex architecture design or strong regularization that limits the capacity of the learned policy. We propose Policy Stitching, a novel framework that facilitates robot transfer learning for novel combinations of robots and tasks. Our key idea is to apply modular policy design and align the latent representations between the modular interfaces. Our method allows direct stitching of the robot and task modules trained separately to form a new policy for fast adaptation. Our simulated and real-world experiments on various 3D manipulation tasks demonstrate the superior zero-shot and few-shot transfer learning performances of our method. Our project website is at: http://generalroboticslab.com/PolicyStitching/ .

Wasserstein Distributionally Robust Policy Evaluation and Learning for Contextual Bandits

Off-policy evaluation and learning are concerned with assessing a given policy and learning an optimal policy from offline data without direct interaction with the environment. Often, the environment in which the data are collected differs from the environment in which the learned policy is applied. To account for the effect of different environments during learning and execution, distributionally robust optimization (DRO) methods have been developed that compute worst-case bounds on the policy values assuming that the distribution of the new environment lies within an uncertainty set. Typically, this uncertainty set is defined based on the KL divergence around the empirical distribution computed from the logging dataset. However, the KL uncertainty set fails to encompass distributions with varying support and lacks awareness of the geometry of the distribution support. As a result, KL approaches fall short in addressing practical environment mismatches and lead to over-fitting to worst-case scenarios. To overcome these limitations, we propose a novel DRO approach that employs the Wasserstein distance instead. While Wasserstein DRO is generally computationally more expensive compared to KL DRO, we present a regularized method and a practical (biased) stochastic gradient descent method to optimize the policy efficiently. We also provide a theoretical analysis of the finite sample complexity and iteration complexity for our proposed method. We further validate our approach using a public dataset that was recorded in a randomized stoke trial.

Policy Evaluation in Distributional LQR

Distributional reinforcement learning (DRL) enhances the understanding of the effects of the randomness in the environment by letting agents learn the distribution of a random return, rather than its expected value as in standard RL. At the same time, a main challenge in DRL is that policy evaluation in DRL typically relies on the representation of the return distribution, which needs to be carefully designed. In this paper, we address this challenge for a special class of DRL problems that rely on linear quadratic regulator (LQR) for control, advocating for a new distributional approach to LQR, which we call \emph{distributional LQR}. Specifically, we provide a closed-form expression of the distribution of the random return which, remarkably, is applicable to all exogenous disturbances on the dynamics, as long as they are independent and identically distributed (i.i.d.). While the proposed exact return distribution consists of infinitely many random variables, we show that this distribution can be approximated by a finite number of random variables, and the associated approximation error can be analytically bounded under mild assumptions. Using the approximate return distribution, we propose a zeroth-order policy gradient algorithm for risk-averse LQR using the Conditional Value at Risk (CVaR) as a measure of risk. Numerical experiments are provided to illustrate our theoretical results.

Risk-Averse Multi-Armed Bandits with Unobserved Confounders: A Case Study in Emotion Regulation in Mobile Health

In this paper, we consider a risk-averse multi-armed bandit (MAB) problem where the goal is to learn a policy that minimizes the risk of low expected return, as opposed to maximizing the expected return itself, which is the objective in the usual approach to risk-neutral MAB. Specifically, we formulate this problem as a transfer learning problem between an expert and a learner agent in the presence of contexts that are only observable by the expert but not by the learner. Thus, such contexts are unobserved confounders (UCs) from the learner's perspective. Given a dataset generated by the expert that excludes the UCs, the goal for the learner is to identify the true minimum-risk arm with fewer online learning steps, while avoiding possible biased decisions due to the presence of UCs in the expert's data.