Stage-dependent integer-binary encoding in factorization-machine black-box optimization

• URL: http://arxiv.org/abs/2606.23188v1
• Date: Mon, 22 Jun 2026 11:36:27 GMT
• Title: Stage-dependent integer-binary encoding in factorization-machine black-box optimization
• Abstract summary: Black-box optimization deals with problems where objective functions lack explicit analytical forms and are expensive to evaluate.<n>We propose a stage-dependent FMQA framework and derive conversion formulas between one-hot and domain-wall QUBO matrices.<n>We evaluate the OhDw variant, which employs one-hot encoding for learning and domain-wall encoding for search.
• Score: 0.612477318852572
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Black-box optimization (BBO) deals with problems where objective functions lack explicit analytical forms and are expensive to evaluate. Factorization machine with quadratic-optimization annealing (FMQA) constructs a surrogate model using a factorization machine (FM) and optimizes it with an Ising machine. Conventional FMQA applies a single integer-binary encoding throughout the optimization process, although the encoding best suited to surrogate learning may differ from the one best suited to Ising-machine solution search. We propose a stage-dependent FMQA framework and derive conversion formulas between one-hot and domain-wall QUBO matrices that preserve the surrogate objective over feasible integer states up to an additive constant. We evaluate the OhDw variant, which employs one-hot encoding for learning and domain-wall encoding for search, on the Rastrigin function with input dimensions N = 2 and 5 and discretization levels q = 61 and 301. Across all conditions, the dominant factor governing optimization performance is the encoding used in the learning stage, with one-hot encoding consistently yielding lower residual errors than domain-wall or binary encoding. The additional benefit of switching to domain-wall encoding for solution search is condition-dependent. For N = 5 and q = 301, OhDw achieves a lower residual error and solutions closer to the global optimum than one-hot-only FMQA, whereas for N = 5 and q = 61 the latter achieves a lower residual error. These results indicate that one-hot encoding in the learning stage is the primary performance driver and that stage-dependent encoding can provide further improvement under finer discretization.

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