Myopically Verifiable Probabilistic Certificates for Safe Control and Learning

This paper addresses the design of safety certificates for stochastic systems, with a focus on ensuring long-term safety through fast real-time control. In stochastic environments, set invariance-based methods that restrict the probability of risk events in infinitesimal time intervals may exhibit significant long-term risks due to cumulative uncertainties/risks. On the other hand, reachability-based approaches that account for the long-term future may require prohibitive computation in real-time decision making. To overcome this challenge involving stringent long-term safety vs. computation tradeoffs, we first introduce a novel technique termed `probabilistic invariance'. This technique characterizes the invariance conditions of the probability of interest. When the target probability is defined using long-term trajectories, this technique can be used to design myopic conditions/controllers with assured long-term safe probability. Then, we integrate this technique into safe control and learning. The proposed control methods efficiently assure long-term safety using neural networks or model predictive controllers with short outlook horizons. The proposed learning methods can be used to guarantee long-term safety during and after training. Finally, we demonstrate the performance of the proposed techniques in numerical simulations.

A Learning and Control Perspective for Microfinance

Microfinance in developing areas such as Africa has been proven to improve the local economy significantly. However, many applicants in developing areas cannot provide adequate information required by the financial institution to make a lending decision. As a result, it is challenging for microfinance institutions to assign credit properly based on conventional policies. In this paper, we formulate the decision-making of microfinance into a rigorous optimization-based framework involving learning and control. We propose an algorithm to explore and learn the optimal policy to approve or reject applicants. We provide the conditions under which the algorithms are guaranteed to converge to an optimal one. The proposed algorithm can naturally deal with missing information and systematically tradeoff multiple objectives such as profit maximization, financial inclusion, social benefits, and economic development. Through extensive simulation of both real and synthetic microfinance datasets, we showed our proposed algorithm is superior to existing benchmarks. To the best of our knowledge, this paper is the first to make a connection between microfinance and control and use control-theoretic tools to optimize the policy with a provable guarantee.