“Differentiable Dynamic Programming for Structured Prediction and Attention”, Arthur Mensch, Mathieu Blondel2018-02-11 (neural net, model-based RL, decision theory; backlinks)⁠:

Dynamic programming (DP) solves a variety of structured combinatorial problems by iteratively breaking them down into smaller subproblems. In spite of their versatility, DP algorithms are usually non-differentiable, which hampers their use as a layer in neural networks trained by backpropagation. To address this issue, we propose to smooth the max operator in the dynamic programming recursion, using a strongly convex regularizer. This allows to relax both the optimal value and solution of the original combinatorial problem, and turns a broad class of DP algorithms into differentiable operators.

Theoretically, we provide a new probabilistic perspective on backpropagating through these DP operators, and relate them to inference in graphical models. We derive two particular instantiations of our framework, a smoothed Viterbi algorithm for sequence prediction and a smoothed DTW (Dynamic Time Warping) algorithm for time-series alignment.

We showcase these instantiations on two structured prediction tasks and on structured and sparse attention for neural machine translation.

In conclusion, our framework offers a novel approach for integrating dynamic programming algorithms into the neural network training process, thereby opening up new possibilities for solving combinatorial optimization problems within a differentiable programming paradigm.

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