Alignment of Large Language models (LLMs) is crucial for safe and trustworthy deployment in applications. Reinforcement learning from human feedback (RLHF) has emerged as an effective technique to align LLMs to human preferences and broader utilities, but it requires updating billions of model parameters, which is computationally expensive. Controlled Decoding, by contrast, provides a mechanism for aligning a model at inference time without retraining. However, single-agent decoding approaches often struggle to adapt to diverse tasks due to the complexity and variability inherent in these tasks. To strengthen the test-time performance w.r.t the target task, we propose a mixture of agent-based decoding strategies leveraging the existing off-the-shelf aligned LLM policies. Treating each prior policy as an agent in the spirit of mixture of agent collaboration, we develop a decoding method that allows for inference-time alignment through a token-level selection strategy among multiple agents. For each token, the most suitable LLM is dynamically chosen from a pool of models based on a long-term utility metric. This policy-switching mechanism ensures optimal model selection at each step, enabling efficient collaboration and alignment among LLMs during decoding. Theoretical analysis of our proposed algorithm establishes optimal performance with respect to the target task represented via a target reward for the given off-the-shelf models. We conduct comprehensive empirical evaluations with open-source aligned models on diverse tasks and preferences, which demonstrates the merits of this approach over single-agent decoding baselines. Notably, Collab surpasses the current SoTA decoding strategy, achieving an improvement of up to 1.56x in average reward and 71.89% in GPT-4 based win-tie rate.

In this paper, we study inverse game theory (resp. inverse multiagent learning) in which the goal is to find parameters of a game's payoff functions for which the expected (resp. sampled) behavior is an equilibrium. We formulate these problems as generative-adversarial (i.e., min-max) optimization problems, for which we develop polynomial-time algorithms to solve, the former of which relies on an exact first-order oracle, and the latter, a stochastic one. We extend our approach to solve inverse multiagent simulacral learning in polynomial time and number of samples. In these problems, we seek a simulacrum, meaning parameters and an associated equilibrium that replicate the given observations in expectation. We find that our approach outperforms the widely-used ARIMA method in predicting prices in Spanish electricity markets based on time-series data.

Mechanism design in resource allocation studies dividing limited resources among self-interested agents whose satisfaction with the allocation depends on privately held utilities. We consider the problem in a payment-free setting, with the aim of maximizing social welfare while enforcing incentive compatibility (IC), i.e., agents cannot inflate allocations by misreporting their utilities. The well-known proportional fairness (PF) mechanism achieves the maximum possible social welfare but incurs an undesirably high exploitability (the maximum unilateral inflation in utility from misreport and a measure of deviation from IC). In fact, it is known that no mechanism can achieve the maximum social welfare and exact incentive compatibility (IC) simultaneously without the use of monetary incentives (Cole et al., 2013). Motivated by this fact, we propose learning an approximate mechanism that desirably trades off the competing objectives. Our main contribution is to design an innovative neural network architecture tailored to the resource allocation problem, which we name Regularized Proportional Fairness Network (RPF-Net). RPF-Net regularizes the output of the PF mechanism by a learned function approximator of the most exploitable allocation, with the aim of reducing the incentive for any agent to misreport. We derive generalization bounds that guarantee the mechanism performance when trained under finite and out-of-distribution samples and experimentally demonstrate the merits of the proposed mechanism compared to the state-of-the-art.

We propose a decentralized market model in which agents can negotiate bilateral contracts. This builds on a similar, but centralized, model of trading networks introduced by Hatfield et al. (2013). Prior work has established that fully-substitutable preferences guarantee the existence of competitive equilibria which can be centrally computed. Our motivation comes from the fact that prices in markets such as over-the-counter markets and used car markets arise from \textit{decentralized} negotiation among agents, which has left open an important question as to whether equilibrium prices can emerge from agent-to-agent bilateral negotiations. We design a best response dynamic intended to capture such negotiations between market participants. We assume fully substitutable preferences for market participants. In this setting, we provide proofs of convergence for sparse markets ({covering many real world markets of interest}), and experimental results for more general cases, demonstrating that prices indeed reach equilibrium, quickly, via bilateral negotiations. Our best response dynamic, and its convergence behavior, forms an important first step in understanding how decentralized markets reach, and retain, equilibrium.

Equivariant neural networks have shown great success in reinforcement learning, improving sample efficiency and generalization when there is symmetry in the task. However, in many problems, only approximate symmetry is present, which makes imposing exact symmetry inappropriate. Recently, approximately equivariant networks have been proposed for supervised classification and modeling physical systems. In this work, we develop approximately equivariant algorithms in reinforcement learning (RL). We define approximately equivariant MDPs and theoretically characterize the effect of approximate equivariance on the optimal Q function. We propose novel RL architectures using relaxed group convolutions and experiment on several continuous control domains and stock trading with real financial data. Our results demonstrate that approximate equivariance matches prior work when exact symmetries are present, and outperforms them when domains exhibit approximate symmetry. As an added byproduct of these techniques, we observe increased robustness to noise at test time.

Large Language Models (LLMs) exhibit impressive capabilities but require careful alignment with human preferences. Traditional training-time methods finetune LLMs using human preference datasets but incur significant training costs and require repeated training to handle diverse user preferences. Test-time alignment methods address this by using reward models (RMs) to guide frozen LLMs without retraining. However, existing test-time approaches rely on trajectory-level RMs which are designed to evaluate complete responses, making them unsuitable for autoregressive text generation that requires computing next-token rewards from partial responses. To address this, we introduce GenARM, a test-time alignment approach that leverages the Autoregressive Reward Model--a novel reward parametrization designed to predict next-token rewards for efficient and effective autoregressive generation. Theoretically, we demonstrate that this parametrization can provably guide frozen LLMs toward any distribution achievable by traditional RMs within the KL-regularized reinforcement learning framework. Experimental results show that GenARM significantly outperforms prior test-time alignment baselines and matches the performance of training-time methods. Additionally, GenARM enables efficient weak-to-strong guidance, aligning larger LLMs with smaller RMs without the high costs of training larger models. Furthermore, GenARM supports multi-objective alignment, allowing real-time trade-offs between preference dimensions and catering to diverse user preferences without retraining.

As artificial intelligence (AI) systems surpass human capabilities in various tasks, ensuring alignment with human values and ethics is crucial. This is especially important for large language models (LLMs), which are trained on diverse datasets that may contain harmful content. Reinforcement Learning from Human Feedback (RLHF) is an effective method for AI alignment, with models like OpenAI's GPT-4, Google's Gemini, and Anthropic Claude showing safe and aligned behaviors. However, the vast majority of the current research in RLHF (Agarwal et al., 2020; Rafailov et al., 2023; Ouyang et al., 2022; Chakraborty et al., 2024; Swamy et al., 2024) focuses on the offline setting, which involves using a fixed dataset of responses generated by the supervised fine-tuned model (SFT), ranked by human experts. Consequently, these methods are inherently offline and heavily reliant on the quality of the offline data generated by the SFT model, which exhibits drawbacks such as insufficient coverage of response-query pairs leading to sub-optimal alignment. To deal with the above shortcomings, recent literature (Guo et al., 2024a; Sharma et al., 2024; Lee et al., 2023; Yuan et al., 2024b) has focused on designing online RLHF algorithms. The setting of online RLHF transcends the constraints of a static offline dataset and aims to address two critical questions: Q1: How should we generate new responses during fine-tuning?

In the context of average-reward reinforcement learning, the requirement for oracle knowledge of the mixing time, a measure of the duration a Markov chain under a fixed policy needs to achieve its stationary distribution, poses a significant challenge for the global convergence of policy gradient methods. This requirement is particularly problematic due to the difficulty and expense of estimating mixing time in environments with large state spaces, leading to the necessity of impractically long trajectories for effective gradient estimation in practical applications. To address this limitation, we consider the Multi-level Actor-Critic (MAC) framework, which incorporates a Multi-level Monte-Carlo (MLMC) gradient estimator. With our approach, we effectively alleviate the dependency on mixing time knowledge, a first for average-reward MDPs global convergence. Furthermore, our approach exhibits the tightest available dependence of $\mathcal{O}\left( \sqrt{\tau_{mix}} \right)$known from prior work. With a 2D grid world goal-reaching navigation experiment, we demonstrate that MAC outperforms the existing state-of-the-art policy gradient-based method for average reward settings.

In this paper, we study the problem of robust cooperative multi-agent reinforcement learning (RL) where a large number of cooperative agents with distributed information aim to learn policies in the presence of \emph{stochastic} and \emph{non-stochastic} uncertainties whose distributions are respectively known and unknown. Focusing on policy optimization that accounts for both types of uncertainties, we formulate the problem in a worst-case (minimax) framework, which is is intractable in general. Thus, we focus on the Linear Quadratic setting to derive benchmark solutions. First, since no standard theory exists for this problem due to the distributed information structure, we utilize the Mean-Field Type Game (MFTG) paradigm to establish guarantees on the solution quality in the sense of achieved Nash equilibrium of the MFTG. This in turn allows us to compare the performance against the corresponding original robust multi-agent control problem. Then, we propose a Receding-horizon Gradient Descent Ascent RL algorithm to find the MFTG Nash equilibrium and we prove a non-asymptotic rate of convergence. Finally, we provide numerical experiments to demonstrate the efficacy of our approach relative to a baseline algorithm.

The conditional mean embedding (CME) encodes Markovian stochastic kernels through their actions on probability distributions embedded within the reproducing kernel Hilbert spaces (RKHS). The CME plays a key role in several well-known machine learning tasks such as reinforcement learning, analysis of dynamical systems, etc. We present an algorithm to learn the CME incrementally from data via an operator-valued stochastic gradient descent. As is well-known, function learning in RKHS suffers from scalability challenges from large data. We utilize a compression mechanism to counter the scalability challenge. The core contribution of this paper is a finite-sample performance guarantee on the last iterate of the online compressed operator learning algorithm with fast-mixing Markovian samples, when the target CME may not be contained in the hypothesis space. We illustrate the efficacy of our algorithm by applying it to the analysis of an example dynamical system.