Mixed Integer Programming (MIP) solvers rely on an array of sophisticated heuristics developed with decades of research to solve large-scale MIP instances encountered in practice. Machine learning offers to automatically construct better heuristics from data by exploiting shared structure among instances in the data. This paper applies learning to the two key sub-tasks of a MIP solver, generating a high-quality joint variable assignment, and bounding the gap in objective value between that assignment and an optimal one.Our approach constructs two corresponding neural network-based components, Neural Diving and Neural Branching, to use in a base MIP solver such as SCIP. Neural Diving learns a deep neural network to generate multiple partial assignments for its integer variables, and the resulting smaller MIPs for un-assigned variables are solved with SCIP to construct high quality joint assignments. Neural Branching learns a deep neural network to make variable selection decisions in branch-and-bound to bound the objective value gap with a small tree. This is done by imitating a new variant of Full Strong Branching we propose that scales to large instances using GPUs. We evaluate our approach on six diverse real-world datasets, including two Google production datasets and MIPLIB, by training separate neural networks on each. Most instances in all the datasets combined have 10 3 − 10 6 variables and constraints after presolve, which is significantly larger than previous learning approaches. Comparing solvers with respect to primal-dual gap averaged over a held-out set of instances, the learning-augmented SCIP is 2× to 10× better on all datasets except one on which it is 10 5 × better, at large time limits. To the best of our knowledge, ours is the first learning approach to demonstrate such large improvements over SCIP on both large-scale real-world application datasets and MIPLIB.

Programming is a powerful and ubiquitous problem-solving tool. Systems that can assist programmers or even generate programs themselves could make programming more productive and accessible. Recent transformer-based neural network models show impressive code generation abilities yet still perform poorly on more complex tasks requiring problem-solving skills, such as competitive programming problems. Here, we introduce AlphaCode, a system for code generation that achieved an average ranking in the top 54.3% in simulated evaluations on recent programming competitions on the Codeforces platform. AlphaCode solves problems by generating millions of diverse programs using specially trained transformer-based networks and then filtering and clustering those programs to a maximum of just 10 submissions. This result marks the first time an artificial intelligence system has performed competitively in programming competitions.

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We study the problem of learning efficient algorithms that strongly generalize in the framework of neural program induction. By carefully designing the input / output interfaces of the neural model and through imitation, we are able to learn models that produce correct results for arbitrary input sizes, achieving strong generalization. Moreover, by using reinforcement learning, we optimize for program efficiency metrics, and discover new algorithms that surpass the teacher used in imitation. With this, our approach can learn to outperform custom-written solutions for a variety of problems, as we tested it on sorting, searching in ordered lists and the NP-complete 0/1 knapsack problem, which sets a notable milestone in the field of Neural Program Induction. As highlights, our learned model can perform sorting perfectly on any input data size we tested on, with O(n log n) complexity, whilst outperforming hand-coded algorithms, including quick sort, in number of operations even for list sizes far beyond those seen during training.Preprint. Under review.