Safe Control of Partially-Observed Linear Time-Varying Systems with Minimal Worst-Case Dynamic Regret

We present safe control of partially-observed linear time-varying systems in the presence of unknown and unpredictable process and measurement noise. We introduce a control algorithm that minimizes dynamic regret, i.e., that minimizes the suboptimality against an optimal clairvoyant controller that knows the unpredictable future a priori. Specifically, our algorithm minimizes the worst-case dynamic regret among all possible noise realizations given a worst-case total noise magnitude. To this end, the control algorithm accounts for three key challenges: safety constraints; partially-observed time-varying systems; and unpredictable process and measurement noise. We are motivated by the future of autonomy where robots will autonomously perform complex tasks despite unknown and unpredictable disturbances leveraging their on-board control and sensing capabilities. To synthesize our minimal-regret controller, we formulate a constrained semi-definite program based on a System Level Synthesis approach for partially-observed time-varying systems. We validate our algorithm in simulated scenarios, including trajectory tracking scenarios of a hovering quadrotor collecting GPS and IMU measurements. Our algorithm is observed to have better performance than either or both the $\mathcal{H}_2$ and $\mathcal{H}_\infty$ controllers, demonstrating a Best of Both Worlds performance.Comment: 8 pages, 3 figure

Bootstrap Confidence Intervals for Medical Costs With Censored Observations

Medical costs data with administratively censored observations often arise in cost-effectiveness studies of treatments for life threatening diseases. Mean of medical costs incurred from the start of a treatment till death or certain timepoint after the implementation of treatment is frequently of interest. In many situations, due to the skewed nature of the cost distribution and non-uniform rate of cost accumulation over time, the currently available normal approximation confidence interval has poor coverage accuracy. In this paper, we proposed a bootstrap confidence interval for the mean of medical costs with censored observations. In simulation studies, we showed that the proposed bootstrap confidence interval had much better coverage accuracy than the normal approximation one when medical costs had a skewed distribution. When there is light censoring on medical costs (less than or equal to 25%), we found that the bootstrap confidence interval based on the simple weighted estimator is preferred due to its simplicity and good coverage accuracy. For heavily censored cost data (censoring rate greater than or equal to 30%) with larger sample sizes (n greater than or equal to 200), the bootstrap confidence intervals based on the partitioned estimator has superior performance in terms of both efficiency and coverage accuracy. We also illustrated the use of our methods in a real example

Efficient Online Learning with Memory via Frank-Wolfe Optimization: Algorithms with Bounded Dynamic Regret and Applications to Control

Projection operations are a typical computation bottleneck in online learning. In this paper, we enable projection-free online learning within the framework of Online Convex Optimization with Memory (OCO-M) -- OCO-M captures how the history of decisions affects the current outcome by allowing the online learning loss functions to depend on both current and past decisions. Particularly, we introduce the first projection-free meta-base learning algorithm with memory that minimizes dynamic regret, i.e., that minimizes the suboptimality against any sequence of time-varying decisions. We are motivated by artificial intelligence applications where autonomous agents need to adapt to time-varying environments in real-time, accounting for how past decisions affect the present. Examples of such applications are: online control of dynamical systems; statistical arbitrage; and time series prediction. The algorithm builds on the Online Frank-Wolfe (OFW) and Hedge algorithms. We demonstrate how our algorithm can be applied to the online control of linear time-varying systems in the presence of unpredictable process noise. To this end, we develop a controller with memory and bounded dynamic regret against any optimal time-varying linear feedback control policy. We validate our algorithm in simulated scenarios of online control of linear time-invariant systems.Comment: The version corrects proofs and updates presentatio