Imitation learning has enabled robots to perform complex, long-horizon tasks in challenging dexterous manipulation settings. As new methods are developed, they must be rigorously evaluated and compared against corresponding baselines through repeated evaluation trials. However, policy comparison is fundamentally constrained by a small feasible sample size (e.g., 10 or 50) due to significant human effort and limited inference throughput of policies. This paper proposes a novel statistical framework for rigorously comparing two policies in the small sample size regime. Prior work in statistical policy comparison relies on batch testing, which requires a fixed, pre-determined number of trials and lacks flexibility in adapting the sample size to the observed evaluation data. Furthermore, extending the test with additional trials risks inducing inadvertent p-hacking, undermining statistical assurances. In contrast, our proposed statistical test is sequential, allowing researchers to decide whether or not to run more trials based on intermediate results. This adaptively tailors the number of trials to the difficulty of the underlying comparison, saving significant time and effort without sacrificing probabilistic correctness. Extensive numerical simulation and real-world robot manipulation experiments show that our test achieves near-optimal stopping, letting researchers stop evaluation and make a decision in a near-minimal number of trials. Specifically, it reduces the number of evaluation trials by up to 40% as compared to state-of-the-art baselines, while preserving the probabilistic correctness and statistical power of the comparison. Moreover, our method is strongest in the most challenging comparison instances (requiring the most evaluation trials); in a multi-task comparison scenario, we save the evaluator more than 200 simulation rollouts.

We approach the fundamental problem of obstacle avoidance for robotic systems via the lens of online learning. In contrast to prior work that either assumes worst-case realizations of uncertainty in the environment or a stationary stochastic model of uncertainty, we propose a method that is efficient to implement and provably grants instance-optimality with respect to perturbations of trajectories generated from an open-loop planner (in the sense of minimizing worst-case regret). The resulting policy adapts online to realizations of uncertainty and provably compares well with the best obstacle avoidance policy in hindsight from a rich class of policies. The method is validated in simulation on a dynamical system environment and compared to baseline open-loop planning and robust Hamilton- Jacobi reachability techniques. Further, it is implemented on a hardware example where a quadruped robot traverses a dense obstacle field and encounters input disturbances due to time delays, model uncertainty, and dynamics nonlinearities.

We consider the problem of generating maximally adversarial disturbances for a given controller assuming only blackbox access to it. We propose an online learning approach to this problem that adaptively generates disturbances based on control inputs chosen by the controller. The goal of the disturbance generator is to minimize regret versus a benchmark disturbance-generating policy class, i.e., to maximize the cost incurred by the controller as well as possible compared to the best possible disturbance generator in hindsight (chosen from a benchmark policy class). In the setting where the dynamics are linear and the costs are quadratic, we formulate our problem as an online trust region (OTR) problem with memory and present a new online learning algorithm (MOTR) for this problem. We prove that this method competes with the best disturbance generator in hindsight (chosen from a rich class of benchmark policies that includes linear-dynamical disturbance generating policies). We demonstrate our approach on two simulated examples: (i) synthetically generated linear systems, and (ii) generating wind disturbances for the popular PX4 controller in the AirSim simulator.

The standard state-of-the-art backend for text-independent speaker recognizers that use i-vectors or x-vectors, is Gaussian PLDA (G-PLDA), assisted by a Gaussianization step involving length normalization. G-PLDA can be trained with both generative or discriminative methods. It has long been known that heavy-tailed PLDA (HT-PLDA), applied without length normalization, gives similar accuracy, but at considerable extra computational cost. We have recently introduced a fast scoring algorithm for a discriminatively trained HT-PLDA backend. This paper extends that work by introducing a fast, variational Bayes, generative training algorithm. We compare old and new backends, with and without length-normalization, with i-vectors and x-vectors, on SRE'10, SRE'16 and SITW.