Murat Firat

Reza Refaei Afshar, Yingqian Zhang, Murat Firat et al.

This paper proposes a Deep Reinforcement Learning (DRL) approach for solving knapsack problem. The proposed method consists of a state aggregation step based on tabular reinforcement learning to extract features and construct states. The state aggregation policy is applied to each problem instance of the knapsack problem, which is used with Advantage Actor Critic (A2C) algorithm to train a policy through which the items are sequentially selected at each time step. The method is a constructive solution approach and the process of selecting items is repeated until the final solution is obtained. The experiments show that our approach provides close to optimal solutions for all tested instances, outperforms the greedy algorithm, and is able to handle larger instances and more flexible than an existing DRL approach. In addition, the results demonstrate that the proposed model with the state aggregation strategy not only gives better solutions but also learns in less timesteps, than the one without state aggregation.

Murat Firat, Guillaume Crognier, Adriana F. Gabor et al.

This paper explores the use of Column Generation (CG) techniques in constructing univariate binary decision trees for classification tasks. We propose a novel Integer Linear Programming (ILP) formulation, based on root-to-leaf paths in decision trees. The model is solved via a Column Generation based heuristic. To speed up the heuristic, we use a restricted instance data by considering a subset of decision splits, sampled from the solutions of the well-known CART algorithm. Extensive numerical experiments show that our approach is competitive with the state-of-the-art ILP-based algorithms. In particular, the proposed approach is capable of handling big data sets with tens of thousands of data rows. Moreover, for large data sets, it finds solutions competitive to CART.