B ayesian Calibration of Win Rate Estimation with LLM Evaluators (2024)

Abstract: Recent advances in large language models (LLMs) show the potential of using LLMs as evaluators for assessing the quality of text generations from LLMs. However, applying LLM evaluators naively to compare different systems can lead to unreliable results due to the inaccuracy and intrinsic bias of LLM evaluators. In order to mitigate this problem, we propose two calibration methods, Bayesian Win-Rate Sampling (BWRS) and Bayesian Dawid-Skene, both of which leverage Bayesian inference to more accurately infer the true win rate of generative language models. We empirically validate our methods on six datasets covering story generation, summarization, and instruction following tasks. We show that both our methods are effective in improving the accuracy of win rate estimation using LLMs as evaluators, offering a promising direction for reliable automatic text quality evaluation.

## introduction evaluating the quality of ai-generated text has been a longstanding and evolving challenge in nlp. in recent years, this challenge has become increasingly crucial due to the growing interest in the field of generative ai. while human judgment is still considered the most reliable form of assessment, common automatic approaches to evaluating quality of ai-generated text include heuristic-based evaluation metrics @xcite @xcite , model-based evaluation metrics @xcite @xcite , and recently, llm-based evaluations @xcite . due to their low cost and high correlation with human preferences, llm-based evaluations are receiving an increasing amount of attention. most previous studies that apply llm evaluators (chiang and lee, 2023a,b; dubois et al., * equal contribution 2024; @xcite attempt to improve the agreement between llm evaluators and human preference by training expert models for evaluation or improving prompting strategies. however, such methods often either require compute-expensive finetuning, or suffer from common problems of llm evaluators such as position bias @xcite , self-preference, and more @xcite . besides, as we will discuss in section 3.2, directly applying a non-perfect llm evaluator will result in a bias problem in the estimation of win rate. in this paper, we attempt to address these challenges by proposing two methods, bwrs and bayesian dawid-skene. our methods leverage bayesian inference to infer the true win rate of one text generator against another using evaluation results of llm evaluators and incorporating optional prior knowledge about human preferences. by employing these methodologies, we observe a closer alignment between llm-generated evaluations and human judgment. 1 the contribution of this paper is threefold: as for evaluating the general capability of llm evaluators, most previous studies @xcite @xcite used correlation coefficients such as pearson's correlation or kendall's tau to measure the preference of different llm evaluators compared with human evaluators. on the application side, llm evaluators are often applied to build llm rankings. @xcite proposed a simple llm evaluation framework by looking at the win rate decided by gpt-4 evaluators on a large number of texts generated by the two generators under the same generation prompts. auto-arena @xcite used llm judge agents to determine the winner of each llm pair. however, as we'll discuss in section 3.2, these methods can lead to biased win rate estimations, especially when the llm evaluators do not align well enough with human preferences. ## methods in this section, we first formalize the problem of applying llms as evaluators. we then point out the bias problem associated with directly applying llm evaluator results, and then propose our methods to address this problem. ## results in this section, we first analyze the evaluator accuracies on our datasets, and then list the results of our experiments, including win rate estimation with no prior, ood prior, and in-distribution prior. we show that both our methods are able to effectively calibrate the estimation of win rate given good estimations of evaluator accuracies. we also show that even with no or ood knowledge of human preference, our methods are still able to perform well overall. ## conclusion in this paper, we identified the bias problem in win rate estimation using non-perfect llm evaluators, and proposed two methods, bwrs and bayesian dawid-skene, in order to address this issue. we then obtained llm evaluation results on six datasets, and used these results to examine the effectiveness of our methods empirically. our results show that both bwrs and bayesian dawid-skene can effectively reduce the error in win rate estimation, especially given good approximations on evaluator accuracies. we also showed that even without in-distribution prior knowledge of human preferences, our methods are still able to effectively calibrate the estimation of win rate under most cases. the effectiveness of our methods manifests the possibility to calibrate the estimation of win rate in a post-hoc manner after llm evaluations are completed, and also enlightens future study on applying annotation models for accurate win rate estimation using llm evaluators.