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Hyperparameter optimization is both a practical issue and an interestingtheoretical problem in training of deep architectures. Despite many recentadvances the most commonly used methods almost universally involve trainingmultiple and decoupled copies of the model, in effect sampling thehyperparameter space. We show that at a negligible additional computationalcost, results can be improved by sampling nonlocal paths instead of points inhyperparameter space. To this end we interpret hyperparameters as controllingthe level of correlated noise in training, which can be mapped to an effectivetemperature. The usually independent instances of the model are coupled andallowed to exchange their hyperparameters throughout the training using thewell established parallel tempering technique of statistical physics. Eachsimulation corresponds then to a unique path, or history, in the jointhyperparameter/model-parameter space. We provide empirical tests of our method,in particular for dropout and learning rate optimization. We observed fastertraining and improved resistance to overfitting and showed a systematicdecrease in the absolute validation error, improving over benchmark results.

Training Deep Neural Networks by optimizing over nonlocal paths in hyperparameter space