
Smart PredictandOptimize for Hard Combinatorial Optimization Problems
Combinatorial optimization assumes that all parameters of the optimizati...
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Ecole: A Library for Learning Inside MILP Solvers
In this paper we describe Ecole (Extensible Combinatorial Optimization L...
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Divide and Learn: A Divide and Conquer Approach for Predict+Optimize
The predict+optimize problem combines machine learning ofproblem coeffic...
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Decision Trees for DecisionMaking under the PredictthenOptimize Framework
We consider the use of decision trees for decisionmaking problems under...
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Melding the DataDecisions Pipeline: DecisionFocused Learning for Combinatorial Optimization
Creating impact in realworld settings requires artificial intelligence ...
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MIPaaL: Mixed Integer Program as a Layer
Machine learning components commonly appear in larger decisionmaking pi...
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Can ML predict the solution value for a difficult combinatorial problem?
We look at whether machine learning can predict the final objective func...
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Discrete solution pools and noisecontrastive estimation for predictandoptimize
Numerous reallife decisionmaking processes involve solving a combinatorial optimization problem with uncertain input that can be estimated from historic data. There is a growing interest in decisionfocused learning methods, where the loss function used for learning to predict the uncertain input uses the outcome of solving the combinatorial problem over a set of predictions. Different surrogate loss functions have been identified, often using a continuous approximation of the combinatorial problem. However, a key bottleneck is that to compute the loss, one has to solve the combinatorial optimisation problem for each training instance in each epoch, which is computationally expensive even in the case of continuous approximations. We propose a different solveragnostic method for decisionfocused learning, namely by considering a pool of feasible solutions as a discrete approximation of the full combinatorial problem. Solving is now trivial through a single pass over the solution pool. We design several variants of a noisecontrastive loss over the solution pool, which we substantiate theoretically and empirically. Furthermore, we show that by dynamically resolving only a fraction of the training instances each epoch, our method performs on par with the state of the art, whilst drastically reducing the time spent solving, hence increasing the feasibility of predictandoptimize for larger problems.
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