Physically Consistent Neural Networks (PCNNs) were recently developed to address these aforementioned issues, ensuring physical consistency while still leveraging NNs to attain state-of-the-art accuracy. However, they remain completely oblivious to the underlying physical laws, which may lead to potentially catastrophic failures if decisions for real-world physical systems are based on them. ![]() On the other hand, classical black-box methods, typically relying on Neural Networks (NNs) nowadays, often achieve impressive performance, even at scale, by deriving statistical patterns from data. While physically sound, classical gray-box models are often cumbersome to identify and scale, and their accuracy might be hindered by their limited expressiveness. With more and more data being collected, data-driven modeling methods have been gaining in popularity in recent years. In contrast, the data-adaptive prior always attains posterior means with small noise limits. Numerical tests show that a fixed prior can lead to a divergent posterior mean in the presence of any of the four types of errors: discretization error, model error, partial observation and wrong noise assumption. Furthermore, we provide a detailed analysis on the computational practice of the data-adaptive prior, and demonstrate it on Toeplitz matrices and integral operators. The data-adaptive prior's covariance is the inversion operator with a hyper-parameter selected adaptive to data by the L-curve method. We introduce a data-adaptive prior to achieve a stable posterior whose mean always has a small noise limit. However, a fixed non-degenerate prior leads to a divergent posterior mean when the observation noise becomes small, if the data induces a perturbation in the eigenspace of zero eigenvalues of the inversion operator. The Bayesian approach overcomes the ill-posedness through a non-degenerate prior. Due to the nonlocal dependence, the inverse problem can be severely ill-posed with a data-dependent singular inversion operator. Thus, learning kernels in operators from data is an inverse problem of general interest. Kernels are efficient in representing nonlocal dependence and they are widely used to design operators between function spaces. We demonstrate the technique in several two-player zero-sum games against a variety of agents, including several AlphaZero-based agents. We introduce ISMCTS-BR, a scalable search-based deep reinforcement learning algorithm for learning a best response to an agent, thereby approximating worst-case performance. Unfortunately, exact computation is infeasible with larger domains, and existing approximations rely on poker-specific knowledge. Prior research in computer poker has examined how to assess such worst-case performance, both exactly and approximately. While valuable, such evaluation typically fails to evaluate robustness to worst-case outcomes. ![]() ![]() In prior games research, agent evaluation often focused on the in-practice game outcomes. To humans, the resulting errors can look like blunders, eroding trust in these agents. Researchers have demonstrated that neural networks are vulnerable to adversarial examples and subtle environment changes, both of which one can view as a form of distribution shift.
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