The (gradient-based) bilevel programming framework is widely used in hyperparameter optimization and has achieved excellent performance empirically. Previous theoretical work mainly focuses on its optimization properties, while leaving the analysis on generalization largely open. This paper attempts to address the issue by presenting an expectation bound w.r.t. the validation set based on uniform stability. Our results can explain some mysterious behaviours of the bilevel programming in practice, for instance, overfitting to the validation set. We also present an expectation bound for the classical cross-validation algorithm. Our results suggest that gradient-based algorithms can be better than cross-validation under certain conditions in a theoretical perspective. Furthermore, we prove that regularization terms in both the outer and inner levels can relieve the overfitting problem in gradient-based algorithms. In experiments on feature learning and data reweighting for noisy labels, we corroborate our theoretical findings.

However,untrusted data sources leavethe services vulnerable to poisoning attacks [5, 28], where adversaries can inject malicious training data to degrade model accuracy.

Classical reactive synthesis approaches aim to synthesize a reactive system that always satisfies a given specifications. These approaches often reduce to playing a two-player zero-sum game where the goal is to synthesize a winning strategy. However, in many pragmatic domains, such as robotics, a winning strategy does not always exist, yet it is desirable for the system to make an effort to satisfy its requirements instead of "giving up". To this end, this paper investigates the notion of admissible strategies, which formalize "doing-your-best", in quantitative reachability games. We show that, unlike the qualitative case, quantitative admissible strategies are history-dependent even for finite payoff functions, making synthesis a challenging task. In addition, we prove that admissible strategies always exist but may produce undesirable optimistic behaviors. To mitigate this, we propose admissible winning strategies, which enforce the best possible outcome while being admissible. We show that both strategies always exist but are not memoryless. We provide necessary and sufficient conditions for the existence of both strategies and propose synthesis algorithms. Finally, we illustrate the strategies on gridworld and robot manipulator domains.