An Optimistic Algorithm for Online Convex Optimization with Adversarial Constraints

We study Online Convex Optimization (OCO) with adversarial constraints, where an online algorithm must make repeated decisions to minimize both convex loss functions and cumulative constraint violations. We focus on a setting where the algorithm has access to predictions of the loss and constraint functions. Our results show that we can improve the current best bounds of $ O(\sqrt{T}) $ regret and $ \tilde{O}(\sqrt{T}) $ cumulative constraint violations to $ O(\sqrt{E_T(f)}) $ and $ \tilde{O}(\sqrt{E_T(g)}) $, respectively, where $ E_T(f) $ and $ E_T(g) $ represent the cumulative prediction errors of the loss and constraint functions. In the worst case, where $ E_T(f) = O(T) $ and $ E_T(g) = O(T) $ (assuming bounded loss and constraint functions), our rates match the prior $ O(\sqrt{T}) $ results. However, when the loss and constraint predictions are accurate, our approach yields significantly smaller regret and cumulative constraint violations. Notably, if the constraint function remains constant over time, we achieve $ \tilde{O}(1) $ cumulative constraint violation, aligning with prior results.

Conformal Decision Theory: Safe Autonomous Decisions from Imperfect Predictions

We introduce Conformal Decision Theory, a framework for producing safe autonomous decisions despite imperfect machine learning predictions. Examples of such decisions are ubiquitous, from robot planning algorithms that rely on pedestrian predictions, to calibrating autonomous manufacturing to exhibit high throughput and low error, to the choice of trusting a nominal policy versus switching to a safe backup policy at run-time. The decisions produced by our algorithms are safe in the sense that they come with provable statistical guarantees of having low risk without any assumptions on the world model whatsoever; the observations need not be I.I.D. and can even be adversarial. The theory extends results from conformal prediction to calibrate decisions directly, without requiring the construction of prediction sets. Experiments demonstrate the utility of our approach in robot motion planning around humans, automated stock trading, and robot manufacturing.