Do LLM Agents  Have Regret? A Case Study in Online Learning and Games

Authors: Chanwoo Park, Xiangyu Liu, Asuman E. Ozdaglar, Kaiqing Zhang
Primary area: foundation or frontier models, including LLMs
Keywords: LLM agents, online learning, repeated games

Abstract:
Large language models (LLMs) have been increasingly employed for (interactive) decision-making, via the development of LLM-based autonomous agents. Despite their emerging successes, the performance of LLM agents in decision-making has not been fully investigated through quantitative metrics, especially in the multi-agent setting when they interact with each other, a typical scenario in real-world LLM-agent applications. To better understand the limits of LLM agents in these interactive environments, we propose to study their interactions in benchmark decision-making settings in online learning and game theory, through the performance metric of regret. We first empirically study the no-regret behaviors of LLMs in canonical non-stochastic online learning problems, as well as the emergence of equilibria when LLM agents interact through playing repeated games. We then provide some theoretical insights into the no-regret behaviors of LLM agents, under certain assumptions on the supervised pre-training and the rationality model of human decision-makers who generate the data. Notably, we also identify (simple) cases where advanced LLMs such as GPT-4 fail to be no-regret. To further promote the no-regret behaviors, we propose a novel unsupervised training loss of regret-loss, which, in contrast to the supervised pre-training loss, does not require the labels of (optimal) actions. Finally, we establish the statistical guarantee of generalization bound for regret-loss minimization, and more importantly, the optimization guarantee that minimizing such a loss may automatically lead to known no-regret learning algorithms, when single-layer self-attention models are used. Our further experiments demonstrate the effectiveness of our regret-loss, especially in addressing the above “regrettable” cases.

Decision: accept (poster)
Reviewer scores: 6, 8, 6, 6

Reviews and discussion:
<thread>
creation date:
1729950484597

thread_type:
official_review

<thread_object>
creator: reviewer_kluz

<content>
summary:
This paper investigates the performance of llm agents in online learning and game-theoretic scenarios. It empirically evaluates no-regret behaviors in pre-trained LLMs like GPT-4 across various online learning settings and repeated games, comparing them with classical no-regret algorithms. The authors introduce a new unsupervised training loss called "regret-loss," designed to enhance no-regret behavior without requiring action labels. It provides theoretical insights connecting pre-training to no-regret algorithms, and presents experimental results validating the proposed approaches.

strengths:
1. It offers a theoretical framework for understanding no-regret behaviors in LLMs and introduces a novel training objective (regret-loss) with provable guarantees.
2. It includes a wide range of experiments with different synthetic & toy-case settings (arbitrary, non-stationary, and bandit feedback environments), comparing LLMs with established no-regret algorithms.

weaknesses:
1. Misalignment of Framework and Problem: The application of online learning and game theory to evaluate LLM agents seems like over-engineering. LLMs are not explicitly designed for decision-making in the classical sense that these fields address (e.g., making repeated decisions based on feedback from an adversarial environment). Using regret minimization as a benchmark for LLM behavior could be seen as an attempt to impose a theoretical construct that may not provide meaningful insights into the actual strengths and weaknesses of LLMs.
2. Lack of Practical Relevance: If the focus is on understanding LLMs' interactive capabilities, other evaluation metrics might be more meaningful. For instance, metrics derived from natural language understanding or task-specific performance might offer more concrete insights into how LLMs perform as interactive agents. The notion of regret, which is central to online learning and game theory, may not be as intuitive or impactful in the context of LLMs used for dialogue, or other applications. There could be alternative frameworks that align better with evaluating and enhancing LLMs. For example, reinforcement learning, interactive learning environments, or even human-in-the-loop evaluations might offer more practical insights than regret-based analysis.

questions:
1. How sensitive are the findings to the choice of synthetic games (win-win, prisoner’s dilemma, unfair, cyclic, biased, and second best) used for experiments?
2. How do the authors validate the importance of the research problem:
    
    "Can we examine and better understand the online and strategic decision-making behaviors of LLMs through the lens of regret"?

    The theoretical results, while rigorous, may feel detached from practical applications. The paper's findings on regret behavior might not translate into concrete benefits for LLM-based systems in the real world, potentially rendering the problem it addresses less relevant. This could make the work feel more like a theoretical exercise than a practical contribution to improving LLM capabilities.
</content>
</thread_object>

</thread>
<thread>
creation date:
1730104656836

thread_type:
official_review

<thread_object>
creator: reviewer_q6rc

<content>
summary:
The paper discusses the use of LLMs for decision-making in both single and multi-agent settings. Their study focuses on understanding the limitations of LLM agents in interactive environments by using regret as a performance metric. Initial empirical investigations assess no-regret behaviors in non-stochastic online learning and the emergence of equilibria in repeated game scenarios. The paper provides theoretical insights into these behaviors based on assumptions about the data’s origin and the rationality of human decision-makers involved in pre-training.

strengths:
1. The paper explores an interesting aspect of using LLM in decision-making tasks. Experimental results are provided.

2. It is interesting that Theorem 5.2 shows a single-layer (linear) self-attention transformer is enough to model no-regret learning algorithms.

3. The paper provides an extensive appendix. The appendix is rich with additional proofs, experimental details, and supplementary discussions. I didn't read all the experimental results and proofs.

weaknesses:
1. It seems not that natural to apply LLMs to solve online decision-making problems, given the existence of classic and well-established algorithms. What are the potential applications? The paper needs to be better motivated to help readers understand the contributions. While the application of LLMs in online decision-making presents intriguing possibilities, the practical implications are not immediately clear. To better engage readers and clarify the significance of this research, the paper could benefit from a more compelling motivation. Specifically, detailing potential real-world applications and explicitly connecting these to the experimental findings would enhance the paper’s relevance and impact.

It's worth considering providing specific examples of potential real-world applications where using LLMs for online decision-making could offer advantages over classical algorithms such as FTPL.

2. The paper does not address the capabilities of state-of-the-art LLM APIs like GPT4 Turbo and o1. Discussing their performance might also offer valuable insights into the scalability and applicability of the proposed methods to more complex decision-making tasks. More detailed analysis of this discrepancy are needed.



Overall, I'd like to raise my score if case studies on real-world application can be provided, with both GPT-4 Turbo and o1 evaluated.

questions:
1. When using GPT4 Turbo and GPT o1 for online decision-making, could the assumption on optimal action labels be relaxed?

2. Why is the regret performance of GPT4 better than single/multi-layer models in the single agent setting, yet vice versa in the multi-agent setting? What factors contribute to this discrepancy in its effectiveness across different settings?

3. What is the technical challenge in the proof of Theorem 5.2? If the result goes beyond simply applying standard learning theory arguments, it's worth highlighting the proof techniques used or created.
</content>
</thread_object>

</thread>
<thread>
creation date:
1730667992882

thread_type:
official_review

<thread_object>
creator: reviewer_d5nu

<content>
summary:
The authors investigate whether LLMs can exhibit no-regret behavior in online learning scenarios. Their main contributions include:

- **Empirical Validation:** The authors empirically show that both commercial and open-source LLMs can achieve no-regret learning in various environments, including dynamic settings and multi-agent games. They demonstrate that LLMs often outperform traditional no-regret algorithms like FTRL and FTPL, with the models effectively incorporating randomization in decision-making.
- **Limitations in Adversarial Scenarios:** The study identifies cases where advanced LLMs, such as GPT models, struggle to achieve sublinear regret, particularly in highly adaptive or adversarial environments. 
- **Theoretical Insights and Enhancements:** The authors provide a theoretical framework explaining how next-token prediction during pretraining enables LLMs to develop capabilities aligned with no-regret algorithms. They also introduce a novel "regret-loss" training objective designed to further strengthen the no-regret properties of LLMs, even in the absence of optimal action labels.

strengths:
The strengths of the paper include: 

- **Comprehensive Empirical Analysis:** The authors conduct a thorough empirical study across diverse environment setups and various LLM models. They evaluate LLM performance in both standard online learning scenarios and multi-agent games, identifying cases where LLMs exhibit no-regret behaviors and outperform classical algorithms like FTRL and FTPL. Importantly, the authors also examine situations where LLMs, such as GPT, fail to achieve sublinear regret in highly adaptive or adversarial environments. This balanced examination provides valuable insights into the conditions under which LLMs succeed or struggle, helping us better understand the decision-making processes and strategic adaptations LLMs employ in online game contexts. 

- **Conduct Ablation Study:** The authors conduct an ablation study to systematically examine the contributions of various components in their proposed framework.

- **Theoretical Justification for No-Regret Behaviors:** The authors offer a theoretical explanation on how next-token prediction pretraining enables LLMs to develop no-regret behaviors in online learning. Under certain structured noise assumption, the optimal behaviors of the LLM under the next-token prediction loss can be related to FTPL.

- The no-regret loss seems to be novel, and enhances the model's performance.

weaknesses:
I found the following weakness points: 

- **Ambiguity in No-Regret Definition and Experimental Setup:** The standard definition of "no-regret" in online learning typically requires that an algorithm achieves sublinear regret for all possible loss sequences, including adversarial ones. However, the authors claim that the LLM behaves as a no-regret algorithm based primarily on experiments involving uniform or Gaussian losses and losses with specific trends, which are not adversarial. This raises some confusion, as these setups do not fully reflect the robustness expected in no-regret algorithms. In fact, the experiments on the "Adaptive loss sequence" seem more directly relevant to evaluating this claim.

- **Lack of Explanation for Model Performance:** Following the previous point, while the authors show that the LLM outperforms traditional no-regret algorithms like FTRL and FTPL, there is limited insight into why this occurs. For instance, the model may be learning the underlying distribution of the loss or fitting specific loss trends, but this is not explicitly demonstrated. Additional analysis on how GPT models achieve superior performance would provide a more comprehensive understanding of these results.

- **Theoretical Limitation**: In Theorem 5.2, you only show the results for $N=1$. If my understanding is correct, this basically means that there is no maximum taken across the input loss sequence $\ell_{1:t}$. Is this also the setup for training the single/multi-layer transformer model under the noisy alternating/adaptive loss as you show in Figure 3.4, or did you use larger $N$ to produce the results? I didn't find the experiment setup for these results in Figure 3.4.

- Building on the previous point, there is one minor thing. I feel that Theorem 4.1 may not fully capture the behavior of LLMs. The empirical results show that GPT models outperform standard no-regret algorithms in more structured tasks but perform significantly worse in adversarial settings. However, what this theorem suggests is that the model after pretraining performs something similar to FTPL. This discrepancy suggests that the theoretical framework might not align with the model's observed strengths and weaknesses across different environments.

However, I still find the contributions to be significant. Hence, I'm open to raising my scores upon the concerns being addressed.

questions:
1. Could the authors clarify the use of the term "no-regret" in this context?
2. In structured, non-adversarial environments (such as linear or sine-trend losses), GPT-4 appears to outperform traditional no-regret algorithms like FTRL/FTPL. Does this suggest that the model may be doing more than no-regret learning, possibly adapting to or fitting the specific trends in the loss sequences through in-context learning?
</content>
</thread_object>

</thread>
<thread>
creation date:
1730712241818

thread_type:
official_review

<thread_object>
creator: reviewer_qxhf

<content>
summary:
This paper studies large language models from a game-theoretic perspective. Observing that LLM-agents are becoming prevalent, they investigate the performance of such LLM agents in terms of regret.

Empirical findings include:

- LLMs exhibit sublinear regret in certain online learning problems
- equilibria emerge when LLM agents interact through repeated games

The authors also develop theory that is consistent with the empirical observations. Finally, the authors propose a new loss function tailored towards regret minimization. They study models optimized under this loss function both theoretically and empirically.

strengths:
- Given the amount of information conveyed, overall the paper is relatively well written, with a sound structure that helps guiding the reader through the large number of findings.
- The contributions appear to be quite substantial. Not being a domain expert, I cannot make a confident judgment as to originality and significance.
- There is a good combination of theory and experiments. The experiments are comprehensive, and the theory appears to be relevant & meaningfully complement the empirical findings.

weaknesses:
- There is a case to be made that the authors are trying to describe too many findings in the main paper. Some figures are hard to read (Figure 3 is a good example of this). The paper ends rather abruptly, with what is essentially a list of pointers to the supplementary material. It appears to me that the layout is deliberately compressed to gain space (e.g., page 10: space above header of Sec. 5.4, space around Eq. 5.3, math fontsize in Thm 5.1).
    - I am genuinely impressed by how comprehensive the study is (there are 77 pages when including the supplementary material). However, I think the main text would benefit from being simplified by omitting certain results. Remember that this is a conference submission with limited space.
    - Again, _conditioned on the set of results presented in the main text_, I don't see many opportunities to improve the organization and presentation, which I find rather good.
- Proposition 1 is problematic. As far as I understand, this proposition rests on an unwritten assumption that the indicators for _difference of regrets is > 0_ are independent. I don't see why this would hold?

questions:
The authors study instruction-tuned models. These typically undergo multiple training stages: a pre-training stage consisting of next-token prediction, and multiple fine-tuning stages that align models with desired behavior.

Have the authors considered comparing the behavior of LLMs at various stages of the training process? This question strikes me as relevant in the context of the discussion in Section 4.2, which makes assumption on the pre-training stage specifically.
</content>
</thread_object>

</thread>
<thread>
creation date:
1732164288754

thread_type:
official_comment

<thread_object>
creator: authors

<content>
title:
General Response

comment:
We appreciate all the feedback from the reviewers, and have addressed them carefully in each individual rebuttal. We here summarize several significant changes we made in the revised paper.

## Real-World Case Studies: 

With the focus on **understanding** the online decision-making capabilities and strategic behaviors of LLMs, our extensive experiments were mostly on synthetic examples (as in other recent works with the same focus), in order to **have controlled experiments, establish some principles, and gain some theoretical insights**. That being said, we appreciate the comments from the reviewers, and have managed to include real-world case studies, on **Sequential Recommendations** and **Interactive Negotiation**, with real-world data. See Section C.11 for more details.

## Clarifications: 

There was some confusion regarding the assumptions for our theoretical and validation framework, experimental setup, and use of some terminologies, for which we have added clarifications and made changes throughout.


Again, we sincerely appreciate the valuable feedback from the reviewers that has helped strengthen our paper. We would be more than happy to answer any further questions that the reviewers may have.

The Authors
</content>
</thread_object>

</thread>


Metareview:
metareview:
Summary:
This work explores the use of large language model (LLM) agents in playing games. The authors conduct experiments across several LLM instances and problem settings, delivering key insights into LLM performance in gaming scenarios, such as demonstrating that most LLM agents can achieve no-regret performance. Furthermore, the authors propose a distributional assumption, the quantal response model, to characterize LLM response distributions and validate its effectiveness through experiments.

Strengths:

- The paper provides a theoretical framework to understand no-regret behaviors in LLMs and introduces a novel training objective, the regret-loss, with provable guarantees.
- The study features a diverse range of experiments, including synthetic and toy-case settings (arbitrary, non-stationary, and bandit feedback environments), and compares LLMs with well-established no-regret algorithms.

Weaknesses:

The presentation can be improved. Notably, the manuscript is approximately 80 pages long, which is unusually lengthy for a conference submission and may hinder accessibility.

Recommendation:
I recommend acceptance based on the strengths mentioned above. Despite the need for a more concise presentation, the paper offers valuable theoretical insights and empirical findings that contribute significantly to the understanding of LLMs in gaming scenarios.