Analysis of Search Heuristics in the Multi-Armed Bandit Setting
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arXiv
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| Format: | Preprint |
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2026
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| author | Brandt, Jasmin Hammer, Barbara Kötzing, Timo Sander, Jurek |
| author_facet | Brandt, Jasmin Hammer, Barbara Kötzing, Timo Sander, Jurek |
| contents | We consider the classic Multi-Armed Bandit setting to understand the exploration/exploitation tradeoffs made by different search heuristics. Since many search heuristics work by comparing different options (in evolutionary algorithms called "individuals"; in the Bandit literature called "arms"), we work with the "Dueling Bandits" setting. In each iteration, a comparison between different arms can be made; in the binary stochastic setting, each arm has a fixed winning probability against any other arm. A Condorcet winner is any arm that beats every other arm with a probability strictly higher than $1/2$.
We show that evolutionary algorithms are rather bad at identifying the Condorcet winner: Even if the Condorcet winner beats every other arm with a probability $1-p$, the (1+1) EA, in its stationary distribution, chooses the Condorcet winner only with constant probability if $p=Ω(1/n)$. By contrast, we show that a simple EDA (based on the Max-Min Ant System with iteration-best update) will choose the Condorcet winner in its maintained distribution with probability $1-Θ(p)$. As a remedy for the (1+1) EA, we show how repeated duels can significantly boost the probability of the Condorcet winner in the stationary distribution. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2604_08109 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Analysis of Search Heuristics in the Multi-Armed Bandit Setting Brandt, Jasmin Hammer, Barbara Kötzing, Timo Sander, Jurek Neural and Evolutionary Computing We consider the classic Multi-Armed Bandit setting to understand the exploration/exploitation tradeoffs made by different search heuristics. Since many search heuristics work by comparing different options (in evolutionary algorithms called "individuals"; in the Bandit literature called "arms"), we work with the "Dueling Bandits" setting. In each iteration, a comparison between different arms can be made; in the binary stochastic setting, each arm has a fixed winning probability against any other arm. A Condorcet winner is any arm that beats every other arm with a probability strictly higher than $1/2$. We show that evolutionary algorithms are rather bad at identifying the Condorcet winner: Even if the Condorcet winner beats every other arm with a probability $1-p$, the (1+1) EA, in its stationary distribution, chooses the Condorcet winner only with constant probability if $p=Ω(1/n)$. By contrast, we show that a simple EDA (based on the Max-Min Ant System with iteration-best update) will choose the Condorcet winner in its maintained distribution with probability $1-Θ(p)$. As a remedy for the (1+1) EA, we show how repeated duels can significantly boost the probability of the Condorcet winner in the stationary distribution. |
| title | Analysis of Search Heuristics in the Multi-Armed Bandit Setting |
| topic | Neural and Evolutionary Computing |
| url | https://arxiv.org/abs/2604.08109 |