# Real-Time Black-Box Optimization for Dynamic Discrete Environments Using Embedded Ising Machines

arXiv: https://arxiv.org/abs/2506.16924 · HTML: https://mlsanity.com/paper/2506.16924/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 15 of its 75 references that are in the map.
- First posted on arXiv 20 Jun 2025.

## Builds on (most cited first, 15 of 15)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Ising formulations of many NP problems](https://mlsanity.com/paper/1302.5843/) (2013)
- [Bayesian Optimization in a Billion Dimensions via Random Embeddings](https://mlsanity.com/paper/1301.1942/) (2013)
- [Deep Learning is Robust to Massive Label Noise](https://mlsanity.com/paper/1705.10694/) (2017)
- [Deep Reinforcement Learning for 5G Networks: Joint Beamforming, Power Control, and Interference Coordination](https://mlsanity.com/paper/1907.00123/) (2019)
- [Application of QUBO solver using black-box optimization to structural design for resonance avoidance](https://mlsanity.com/paper/2204.04906/) (2022)
- [Statistical Properties of the log-cosh Loss Function Used in Machine Learning](https://mlsanity.com/paper/2208.04564/) (2022)
- [Online non-convex optimization with imperfect feedback](https://mlsanity.com/paper/2010.08496/) (2020)
- [Black-box optimization for integer-variable problems using Ising machines and factorization machines](https://mlsanity.com/paper/2209.01016/) (2022)
- [Factored Bandits](https://mlsanity.com/paper/1807.01488/) (2018)
- [Hedging using reinforcement learning: Contextual k-Armed Bandit versus Q-learning](https://mlsanity.com/paper/2007.01623/) (2020)
- [Lossy compression of matrices by black-box optimisation of mixed integer nonlinear programming](https://mlsanity.com/paper/2204.10579/) (2022)
- [Correlation-diversified portfolio construction by finding maximum independent set in large-scale market graph](https://mlsanity.com/paper/2308.04769/) (2023)
- [Efficient and Scalable Architecture for Multiple-chip Implementation of Simulated Bifurcation Machines](https://mlsanity.com/paper/2311.17370/) (2023)
- [Enhancing In-vehicle Multiple Object Tracking Systems with Embeddable Ising Machines](https://mlsanity.com/paper/2410.14093/) (2024)

## Built on by (most cited first, 2 of 2)

- [SWIFT-FMQA: Enhancing Factorization Machine with Quadratic-Optimization Annealing via Sliding Window](https://mlsanity.com/paper/2507.21024/) (2025)
- [Subsampling Factorization Machine Annealing](https://mlsanity.com/paper/2508.08778/) (2025)

## Abstract (arXiv)

Many real-time systems require the optimization of discrete variables. Black-box optimization (BBO) algorithms and multi-armed bandit (MAB) algorithms perform optimization by repeatedly taking actions and observing the corresponding instant rewards without any prior knowledge. Recently, a BBO method using an Ising machine has been proposed to find the best action that is represented by a combination of discrete values and maximizes the instant reward in static environments. In contrast, dynamic environments, where real-time systems operate, necessitate MAB algorithms that maximize the average reward over multiple trials. However, due to the enormous number of actions resulting from the combinatorial nature of discrete optimization, conventional MAB algorithms cannot effectively optimize dynamic, discrete environments. Here, we show a heuristic MAB method for dynamic, discrete environments by extending the BBO method, in which an Ising machine effectively explores the actions while considering interactions between variables and changes in dynamic environments. We demonstrate the dynamic adaptability of the proposed method in a wireless communication system with moving users.