Overconfidence in deep neural networks could easily lead to deployments where predictions are made that should have been withheld. Figure 7: ResNet-50 trained onCIFAR-10 using focal lossγ = 0,3,4,5. Similarly, the confidence of the top predicted classˆy (for the training sample) isdenoted byˆptrain,top and theaverage equivalent inabinbyCtrain,top. Forthe training set, we care only about the confidence ofthe "true class"ˆptrain,true asthat isthe quantity which gets manipulated by some loss function. For validation set, on the other hand, we care about the confidence of the "top predicted class".

This success stems from focal loss regularizing the entropyofthe model'sprediction (controlled by the parameterγ), thereby reining in the model's overconfidence.

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.