Do LLM Agents Have Regret? This Machine Learning Research from MIT and the University of Maryland Presents a Case Study on Online Learning and Games

Large Language Models (LLMs) have been increasingly employed for (interactive) decision-making through the model development of LLM-based agents. LLMs have shown remarkable successes in embodied AI, natural science, and social science applications in recent years. LLMs have also exhibited remarkable potential in solving various games. These exciting empirical successes require rigorous examination and understanding through a theoretical lens of decision-making. However, the performance of LLM agents in decision-making has yet to be 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.

Thus, it is natural to ask:┬áIs it possible to examine and better understand LLMs’ online and strategic decision-making behaviors through the lens of regret?

The impressive capability of LLMs for reasoning has inspired an enhancing line of research on how LLM-based autonomous agents interact with the environment by taking actions repeatedly/sequentially based on the feedback they receive. Some significant promises have been shown from a planning perspective. In particular, for embodied AI applications, e.g., robotics, LLMs have achieved impressive performance when used as the controller for decision-making. However, the performance of decision-making has yet to be rigorously characterized via the regret metric in these works. Recently, some researchers have proposed a principled architecture for LLM-agent, with provable regret guarantees in stationary and stochastic decision-making environments, under the Bayesian adaptive Markov decision processes framework.

To better understand the limits of LLM agents in these interactive environments, researchers from MIT and the University of Maryland propose to study their interactions in benchmark decision-making settings in online learning and game theory through the performance metric of regret. They propose a unique unsupervised training loss of regret-loss, which, in contrast to the supervised pre-training loss, does not require the labels of (optimal) actions. Then, they established the statistical guarantee of generalization bound for regret-loss minimization, followed by the optimization guarantee that minimizing such a loss may automatically lead to known no-regret learning algorithms.

Researchers propose two frameworks to rigorously validate the no-regret behavior of algorithms over a finite T, which might be of independent interest: a Trend-checking framework and a Regression-based framework. In the Trend-checking framework, they defined  H0 and H1, which denote the null and alternative hypotheses, respectively. The notion of convergence is related to T Ôćĺ Ôł× by definition, making it challenging to verify directly. As an alternative, they propose a more tractable hypothesis. They propose an alternative approach in a Regression-based framework by fitting the data with regression. In particular, one can use the data to fit a linear function.

In the experiments, They compare GPT-4 with well-known no-regret algorithms, FTRL with entropy regularization, and FTPL with Gaussian perturbations (with tuned parameters). These pre-trained LLMs can achieve no regret and often have smaller regrets than these baselines. While comparing the performance of pre-trained LLMs with that of the counterparts of FTRL with bandit feedback, e.g., EXP3 and the bandit-version of FTPL, where GPT-4 consistently achieves lower regret. Regret of GPT-3.5 Turbo/GPT-4 for repeated games of 3 different game sizes, where both statistical frameworks validate the sublinear regret. 

In conclusion, the researchers from MIT and the University of Maryland studied the online decision-making and strategic behaviors of LLMs quantitatively through the metric of regret. They examined and validated the no-regret behavior of several representative pre-trained LLMs in benchmark online learning and game settings. They then provide theoretical insights into the no-regret behavior by connecting pre-trained LLMs to the follow-the-perturbed-leader algorithm in online learning under certain assumptions. They also identified (simple) cases where pre-trained LLMs fail to be no-regret. They thus proposed a new unsupervised training loss, regret-loss, to provably promote the no-regret behavior of Transformers without the labels of (optimal) actions.

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