Ashwin Verma

Farbod Siahkali, Ashwin Verma, Vijay Gupta

Conformal prediction (CP) offers distribution-free marginal coverage guarantees under an exchangeability assumption, but these guarantees can fail if the data distribution shifts. We analyze the use of pseudo-calibration as a tool to counter this performance loss under a bounded label-conditional covariate shift model. Using tools from domain adaptation, we derive a lower bound on target coverage in terms of the source-domain loss of the classifier and a Wasserstein measure of the shift. Using this result, we provide a method to design pseudo-calibrated sets that inflate the conformal threshold by a slack parameter to keep target coverage above a prescribed level. Finally, we propose a source-tuned pseudo-calibration algorithm that interpolates between hard pseudo-labels and randomized labels as a function of classifier uncertainty. Numerical experiments show that our bounds qualitatively track pseudo-calibration behavior and that the source-tuned scheme mitigates coverage degradation under distribution shift while maintaining nontrivial prediction set sizes.

Vinay Kanakeri, Shivam Bajaj, Ashwin Verma et al.

It is known that reinforcement learning (RL) is data-hungry. To improve sample-efficiency of RL, it has been proposed that the learning algorithm utilize data from 'approximately similar' processes. However, since the process models are unknown, identifying which other processes are similar poses a challenge. In this work, we study this problem in the context of the benchmark Linear Quadratic Regulator (LQR) setting. Specifically, we consider a setting with multiple agents, each corresponding to a copy of a linear process to be controlled. The agents' local processes can be partitioned into clusters based on similarities in dynamics and tasks. Combining ideas from sequential elimination and zeroth-order policy optimization, we propose a new algorithm that performs simultaneous clustering and learning to output a personalized policy (controller) for each cluster. Under a suitable notion of cluster separation that captures differences in closed-loop performance across systems, we prove that our approach guarantees correct clustering with high probability. Furthermore, we show that the sub-optimality gap of the policy learned for each cluster scales inversely with the size of the cluster, with no additional bias, unlike in prior works on collaborative learning-based control. Our work is the first to reveal how clustering can be used in data-driven control to learn personalized policies that enjoy statistical gains from collaboration but do not suffer sub-optimality due to inclusion of data from dissimilar processes. From a distributed implementation perspective, our method is attractive as it incurs only a mild logarithmic communication overhead.