Study on Using Reinforcement Learning for the Monotone Boolean Reconstruction
This paper investigates the feasibility of using reinforcement learning to solve combinatorial optimization problems, in particular, the problem of query-based monotone Boolean function reconstruction. The monotone Boolean function reconstruction problem is a typical combinatorial problem that recon...
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| Vydáno v: | Informatica (Ljubljana) Ročník 48; číslo 4; s. 521 - 532 |
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| Hlavní autoři: | , , |
| Médium: | Journal Article |
| Jazyk: | angličtina |
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Ljubljana
Slovenian Society Informatika / Slovensko drustvo Informatika
07.01.2025
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| ISSN: | 0350-5596, 1854-3871 |
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| Abstract | This paper investigates the feasibility of using reinforcement learning to solve combinatorial optimization problems, in particular, the problem of query-based monotone Boolean function reconstruction. The monotone Boolean function reconstruction problem is a typical combinatorial problem that reconstructs the function unambiguously with a minimum number of queries about the value of the function at the defined points, based on the monotonicity of the function. The Shannon complexity of the problem is of the order of 2n/\[n, and the solution algorithm relies on complex constructions, which also add complexity in the form of memory and time. Additionally, there are problems of partial reconstruction, e.g., in the mining of associative rules, which do not fit into the developed solution formats. This necessitates exploring heuristic domains to attract additional resources to solve the problem. To this end, all elements of reinforcement learning - environment, agent, policy, etc. - are designed, and both exact and approximate algorithms are given to perform the necessary structural data transformations, as well as to calculate the reward, the value, and other operational data of the algorithm. The focal point of the considerations is a subclass of monotone Boolean functions related to the well-known shadow minimization theorem of layer-by-layer characterized functions. Preliminary experiments have been started and they require follow-up intensive actions. |
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| AbstractList | This paper investigates the feasibility of using reinforcement learning to solve combinatorial optimization problems, in particular, the problem of query-based monotone Boolean function reconstruction. The monotone Boolean function reconstruction problem is a typical combinatorial problem that reconstructs the function unambiguously with a minimum number of queries about the value of the function at the defined points, based on the monotonicity of the function. The Shannon complexity of the problem is of the order of 2n/\[n, and the solution algorithm relies on complex constructions, which also add complexity in the form of memory and time. Additionally, there are problems of partial reconstruction, e.g., in the mining of associative rules, which do not fit into the developed solution formats. This necessitates exploring heuristic domains to attract additional resources to solve the problem. To this end, all elements of reinforcement learning - environment, agent, policy, etc. - are designed, and both exact and approximate algorithms are given to perform the necessary structural data transformations, as well as to calculate the reward, the value, and other operational data of the algorithm. The focal point of the considerations is a subclass of monotone Boolean functions related to the well-known shadow minimization theorem of layer-by-layer characterized functions. Preliminary experiments have been started and they require follow-up intensive actions. |
| Author | Sahakyan, Hasmik Aslanyan, Levon Katona, Gyula |
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| Copyright | 2024. This work is published under https://creativecommons.org/licenses/by/3.0/ (the “License”). Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License. |
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| DOI | 10.31449/inf.v48i4.4804 |
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| SubjectTerms | Algorithms Approximation Artificial intelligence Boolean Boolean functions Codes Combinatorial analysis Complexity Data mining Decision making Decision trees Investigations Machine learning Optimization Queries Reconstruction Traveling salesman problem |
| Title | Study on Using Reinforcement Learning for the Monotone Boolean Reconstruction |
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