A State Aggregation Approach for Solving Knapsack Problem with Deep Reinforcement Learning

Reza Refaei Afshar, Yingqian Zhang, Murat Firat, Uzay Kaymak
Proceedings of The 12th Asian Conference on Machine Learning, PMLR 129:81-96, 2020.

Abstract

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.

Cite this Paper

BibTeX
@InProceedings{pmlr-v129-refaei-afshar20a, title = {A State Aggregation Approach for Solving Knapsack Problem with Deep Reinforcement Learning}, author = {Refaei Afshar, Reza and Zhang, Yingqian and Firat, Murat and Kaymak, Uzay}, booktitle = {Proceedings of The 12th Asian Conference on Machine Learning}, pages = {81--96}, year = {2020}, editor = {Pan, Sinno Jialin and Sugiyama, Masashi}, volume = {129}, series = {Proceedings of Machine Learning Research}, month = {18--20 Nov}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v129/refaei-afshar20a/refaei-afshar20a.pdf}, url = {https://proceedings.mlr.press/v129/refaei-afshar20a.html}, abstract = {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.} }
Endnote
%0 Conference Paper %T A State Aggregation Approach for Solving Knapsack Problem with Deep Reinforcement Learning %A Reza Refaei Afshar %A Yingqian Zhang %A Murat Firat %A Uzay Kaymak %B Proceedings of The 12th Asian Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2020 %E Sinno Jialin Pan %E Masashi Sugiyama %F pmlr-v129-refaei-afshar20a %I PMLR %P 81--96 %U https://proceedings.mlr.press/v129/refaei-afshar20a.html %V 129 %X 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.
APA
Refaei Afshar, R., Zhang, Y., Firat, M. & Kaymak, U.. (2020). A State Aggregation Approach for Solving Knapsack Problem with Deep Reinforcement Learning. Proceedings of The 12th Asian Conference on Machine Learning, in Proceedings of Machine Learning Research 129:81-96 Available from https://proceedings.mlr.press/v129/refaei-afshar20a.html.

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