Conformal Prediction (CP) is a powerful statistical machine learning tool to construct uncertainty sets with coverage guarantees, which has fueled its extensive adoption in generating prediction regions for decision-making tasks, e.g., Trajectory Optimization (TO) in uncertain environments. However, existing methods predominantly employ a sequential scheme, where decisions rely unidirectionally on the prediction regions, and consequently the information from decision-making fails to be fed back to instruct CP. In this paper, we propose a novel Feedback-Based CP (Fb-CP) framework for shrinking-horizon TO with a joint risk constraint over the entire mission time. Specifically, a CP-based posterior risk calculation method is developed by fully leveraging the realized trajectories to adjust the posterior allowable risk, which is then allocated to future times to update prediction regions. In this way, the information in the realized trajectories is continuously fed back to the CP, enabling attractive feedback-based adjustments of the prediction regions and a provable online improvement in trajectory performance. Furthermore, we theoretically prove that such adjustments consistently maintain the coverage guarantees of the prediction regions, thereby ensuring provable safety. Additionally, we develop a decision-focused iterative risk allocation algorithm with theoretical convergence analysis for allocating the posterior allowable risk which closely aligns with Fb-CP. Furthermore, we extend the proposed method to handle distribution shift. The effectiveness and superiority of the proposed method are demonstrated through benchmark experiments.

Amid ongoing economic anxieties, BLK and other companies are giving away basic essentials to appeal to the public. While Gen Z catches a lot of flack for being single, or even antisocial, there's a brutal economic reality underscoring why some people aren't going out: They simply don't have the disposable income . Dating apps, already struggling to maintain user bases due to enshittification and a lack of quality matches, are contending with this affordability crisis. In a dystopian sign of the times, BLK, the app for Black singles, announced on Wednesday that it is giving away free gas in an attempt to incentivize people to go on dates. As part of the promotion, BLK is providing $500 gas gift cards to 10 people who download the app and tag three friends in the campaign post across its social channels.

This paper studies first-order policy optimization for robust average cost Markov decision processes (MDPs). Specifically, we focus on ergodic Markov chains. For robust average cost MDPs, the goal is to optimize the worst-case average cost over an uncertainty set of transition kernels. We first develop a sub-gradient of the robust average cost. Based on the sub-gradient, a robust policy mirror descent approach is further proposed. To characterize its iteration complexity, we develop a lower bound on the difference of robust average cost between two policies and further show that the robust average cost satisfies the PL-condition. We then show that with increasing step size, our robust policy mirror descent achieves a linear convergence rate in the optimality gap, and with constant step size, our algorithm converges to an $\epsilon$-optimal policy with an iteration complexity of $\mathcal{O}(1/\epsilon)$. The convergence rate of our algorithm matches with the best convergence rate of policy-based algorithms for robust MDPs. Moreover, our algorithm is the first algorithm that converges to the global optimum with general uncertainty sets for robust average cost MDPs. We provide simulation results to demonstrate the performance of our algorithm.

Importantly, E2 is bounded independently ofS.

This article revisits the 20-year-old neural fitted Q-iteration (NFQ) algorithm on its classical CartPole benchmark. NFQ was a pioneering approach towards modern Deep Reinforcement Learning (Deep RL) in applying multi-layer neural networks to reinforcement learning for real-world control problems. We explore the algorithm's conceptual simplicity and its transition from online to batch learning, which contributed to its stability. Despite its initial success, NFQ required extensive tuning and was not easily reproducible on real-world control problems. We propose a modernized variant NFQ2.0 and apply it to the CartPole task, concentrating on a real-world system build from standard industrial components, to investigate and improve the learning process's repeatability and robustness. Through ablation studies, we highlight key design decisions and hyperparameters that enhance performance and stability of NFQ2.0 over the original variant. Finally, we demonstrate how our findings can assist practitioners in reproducing and improving results and applying deep reinforcement learning more effectively in industrial contexts.

We illustrate the online optimization process of RCL in Figure 1. We set b = 10 and A = I for the cost function in Eqn. The testing process is almost instant and takes less than 1 second. It does not use robustification during online optimization. By Theorem 4.1, there is a trade-off (governed by ML predictions for those problem instances that are adversarial to ROBD.

We study a challenging form of Smoothed Online Convex Optimization, a.k.a.