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We address the problem of interpretability in iterative game solving for imperfect-information games such as poker. This lack of interpretability has two main sources: first, the use of an uninterpretable feature representation, and second, the use of black box methods such as neural networks, for the fitting procedure. In this paper, we present advances on both fronts. Namely, first we propose a novel, compact, and easy-to-understand game-state feature representation for Heads-up No-limit (HUNL) Poker. Second, we make use of globally optimal decision trees, paired with a counterfactual regret minimization (CFR) self-play algorithm, to train our poker bot which produces an entirely interpretable agent. Through experiments against Slumbot, the winner of the most recent Annual Computer Poker Competition, we demonstrate that our approach yields a HUNL Poker agent that is capable of beating the Slumbot. Most exciting of all, the resulting poker bot is highly interpretable, allowing humans to learn from the novel strategies it discovers.

This paper presents a novel holistic deep learning framework that simultaneously addresses the challenges of vulnerability to input perturbations, overparametrization, and performance instability from different train-validation splits. The proposed framework holistically improves accuracy, robustness, sparsity, and stability over standard deep learning models, as demonstrated by extensive experiments on both tabular and image data sets. The results are further validated by ablation experiments and SHAP value analysis, which reveal the interactions and trade-offs between the different evaluation metrics. To support practitioners applying our framework, we provide a prescriptive approach that offers recommendations for selecting an appropriate training loss function based on their specific objectives. All the code to reproduce the results can be found at https://github.com/kimvc7/HDL .

We provide a methodology for learning sparse statistical models that use as features all possible multiplicative interactions among an underlying atomic set of features. While the resulting optimization problems are exponentially sized, our methodology leads to algorithms that can often solve these problems exactly or provide approximate solutions based on combining highly correlated features. We also introduce an algorithmic paradigm, the Fine Control Kernel framework, so named because it is based on Fenchel Duality and is reminiscent of kernel methods. Its theory is tailored to large sparse learning problems, and it leads to efficient feature screening rules for interactions. These rules are inspired by the Apriori algorithm for market basket analysis -- which also falls under the purview of Fine Control Kernels, and can be applied to a plurality of learning problems including the Lasso and sparse matrix estimation. Experiments on biomedical datasets demonstrate the efficacy of our methodology in deriving algorithms that efficiently produce interactions models which achieve state-of-the-art accuracy and are interpretable.

This paper presents a novel holistic deep learning framework that simultaneously addresses the challenges of vulnerability to input perturbations, overparametrization, and performance instability from different train-validation splits. The proposed framework holistically improves accuracy, robustness, sparsity, and stability over standard deep learning models, as demonstrated by extensive experiments on both tabular and image data sets. The results are further validated by ablation experiments and SHAP value analysis, which reveal the interactions and trade-offs between the different evaluation metrics. To support practitioners applying our framework, we provide a prescriptive approach that offers recommendations for selecting an appropriate training loss function based on their specific objectives. All the code to reproduce the results can be found at https://github.com/kimvc7/HDL.

Achievable information rates (AIRs) of wideband optical communication systems using ~40 nm (~5 THz) EDFA and ~100 nm (~12.5 THz) distributed Raman amplification are estimated based on a first-order perturbation analysis. The AIRs of each individual channel have been evaluated for DP-64QAM, DP-256QAM, and DP-1024QAM modulation formats. The impact of full-field nonlinear compensation (FF-NLC) and probabilistically shaped constellations using a Maxwell-Boltzmann distribution were studied and compared to electronic dispersion compensation. It is found that a probabilistically shaped DP-1024QAM constellation combined with FF-NLC yields AIRs of ~75 Tbit/s for the EDFA scheme and ~223 Tbit/s for the Raman amplification scheme over 2000 km standard single mode fibre transmission.