Many applications seek to optimize LLM outputs at test time by iteratively proposing, scoring, and refining candidates over a discrete output space. Existing methods use a calibrated scalar evaluator for the target objective to guide search, but for many tasks such scores are unavailable, too sparse, or unreliable. Pairwise comparisons, by contrast, are often easier to elicit, still provide useful signal on improvement directions, and can be obtained from the LLM itself without external supervision. Building on this observation, we introduce Duel-Evolve, an evolutionary optimization algorithm that replaces external scalar rewards with pairwise preferences elicited from the same LLM used to generate candidates. Duel-Evolve aggregates these noisy candidate comparisons via a Bayesian Bradley-Terry model, yielding uncertainty-aware estimates of candidate quality. These quality estimates guide allocation of the comparison budget toward plausible optima using Double Thompson Sampling, as well as selection of high-quality parents to generate improved candidates. We evaluate Duel-Evolve on MathBench, where it achieves 20 percentage points higher accuracy over existing methods and baselines, and on LiveCodeBench, where it improves over comparable iterative methods by over 12 percentage points. Notably, the method requires no reward model, no ground-truth labels during search, and no hand-crafted scoring function. Results show that pairwise self-preferences provide strong optimization signal for test-time improvement over large, discrete output spaces.
Figures & tables
Figure 1: Duel-Evolve approximates Double Thompson Sampling (DTS) over a combinatorial space. At round t , DTS maintains a posterior p(θ∣D1:t) over latent utilities θ=(θy)y∈Y given comparison history D1:t={(yi,yj,cij)} , and selects the next duel by sampling ya,yb∼pt∗(y)=P(y=argmaxy′θy′∣D1:t) . Duel-Evolve approximates posterior inference by fitting a Bradley–Terry model on the evaluated pool Et with a Laplace approximation, yielding per-candidate summaries (μi,t,σi,t) (§ 2.3.1 ); it then approximates maximizer-focused sampling by Thompson-sampling duels and parents At from a pruned survivor set St⊆Et , and proposing children via a conditioned LLM generator y∼pϕ(y∣x,{(yi,μi,t)}yi∈At) (§ 2.3.2 –§ 2.3.3 ).
Figure 2: MathBench accuracy over 150 generations. Left: Duel-Evolve performance stratified by difficulty level ( Middle , High , College ). Middle: Method comparison over generations: non-iterative baselines (Zero-shot CoT, Few-shot CoT, Self-consistency, and Best-of- N ) remain flat, while iterative methods (Feedback Descent, GEPA, and Duel-Evolve ) improve over time. Right: Final accuracy across methods. Duel-Evolve achieves the best performance.
Figure 3: LiveCodeBench accuracy over 200 generations. Left: Duel-Evolve performance stratified by difficulty level ( Easy , Medium , Hard ). Middle: Method comparison over generations: static baselines (Zero-shot CoT, Few-shot CoT, Self-consistency, and Best-of- N ) are flat, while iterative methods (Feedback Descent, GEPA and Duel-Evolve ) improve over time. Right: Final accuracy across methods. Duel-Evolve achieves the best performance.
State Key Laboratory of AI Safety, Institute of Computing Technology, Chinese Academy of Sciences. · School of Computer Science and Technology, University of Chinese Academy of Sciences. · Beijing Academy of Artificial Intelligence. +1