Offline Regularised Reinforcement Learning for Large Language Models Alignment

The dominant framework for alignment of large language models (LLM), whether through reinforcement learning from human feedback or direct preference optimisation, is to learn from preference data. This involves building datasets where each element is a quadruplet composed of a prompt, two independent responses (completions of the prompt) and a human preference between the two independent responses, yielding a preferred and a dis-preferred response. Such data is typically scarce and expensive to collect. On the other hand, \emph{single-trajectory} datasets where each element is a triplet composed of a prompt, a response and a human feedback is naturally more abundant. The canonical element of such datasets is for instance an LLM's response to a user's prompt followed by a user's feedback such as a thumbs-up/down. Consequently, in this work, we propose DRO, or \emph{Direct Reward Optimisation}, as a framework and associated algorithms that do not require pairwise preferences. DRO uses a simple mean-squared objective that can be implemented in various ways. We validate our findings empirically, using T5 encoder-decoder language models, and show DRO's performance over selected baselines such as Kahneman-Tversky Optimization (KTO). Thus, we confirm that DRO is a simple and empirically compelling method for single-trajectory policy optimisation.

Super-Exponential Regret for UCT, AlphaGo and Variants

We improve the proofs of the lower bounds of Coquelin and Munos (2007) that demonstrate that UCT can have $\exp(\dots\exp(1)\dots)$ regret (with $\Omega(D)$ exp terms) on the $D$-chain environment, and that a `polynomial' UCT variant has $\exp_2(\exp_2(D - O(\log D)))$ regret on the same environment -- the original proofs contain an oversight for rewards bounded in $[0, 1]$, which we fix in the present draft. We also adapt the proofs to AlphaGo's MCTS and its descendants (e.g., AlphaZero, Leela Zero) to also show $\exp_2(\exp_2(D - O(\log D)))$ regret.

Human Alignment of Large Language Models through Online Preference Optimisation

Ensuring alignment of language models' outputs with human preferences is critical to guarantee a useful, safe, and pleasant user experience. Thus, human alignment has been extensively studied recently and several methods such as Reinforcement Learning from Human Feedback (RLHF), Direct Policy Optimisation (DPO) and Sequence Likelihood Calibration (SLiC) have emerged. In this paper, our contribution is two-fold. First, we show the equivalence between two recent alignment methods, namely Identity Policy Optimisation (IPO) and Nash Mirror Descent (Nash-MD). Second, we introduce a generalisation of IPO, named IPO-MD, that leverages the regularised sampling approach proposed by Nash-MD. This equivalence may seem surprising at first sight, since IPO is an offline method whereas Nash-MD is an online method using a preference model. However, this equivalence can be proven when we consider the online version of IPO, that is when both generations are sampled by the online policy and annotated by a trained preference model. Optimising the IPO loss with such a stream of data becomes then equivalent to finding the Nash equilibrium of the preference model through self-play. Building on this equivalence, we introduce the IPO-MD algorithm that generates data with a mixture policy (between the online and reference policy) similarly as the general Nash-MD algorithm. We compare online-IPO and IPO-MD to different online versions of existing losses on preference data such as DPO and SLiC on a summarisation task.

Model-free Posterior Sampling via Learning Rate Randomization

In this paper, we introduce Randomized Q-learning (RandQL), a novel randomized model-free algorithm for regret minimization in episodic Markov Decision Processes (MDPs). To the best of our knowledge, RandQL is the first tractable model-free posterior sampling-based algorithm. We analyze the performance of RandQL in both tabular and non-tabular metric space settings. In tabular MDPs, RandQL achieves a regret bound of order $\widetilde{\mathcal{O}}(\sqrt{H^{5}SAT})$, where $H$ is the planning horizon, $S$ is the number of states, $A$ is the number of actions, and $T$ is the number of episodes. For a metric state-action space, RandQL enjoys a regret bound of order $\widetilde{\mathcal{O}}(H^{5/2} T^{(d_z+1)/(d_z+2)})$, where $d_z$ denotes the zooming dimension. Notably, RandQL achieves optimistic exploration without using bonuses, relying instead on a novel idea of learning rate randomization. Our empirical study shows that RandQL outperforms existing approaches on baseline exploration environments.

Representations and Exploration for Deep Reinforcement Learning using Singular Value Decomposition

Representation learning and exploration are among the key challenges for any deep reinforcement learning agent. In this work, we provide a singular value decomposition based method that can be used to obtain representations that preserve the underlying transition structure in the domain. Perhaps interestingly, we show that these representations also capture the relative frequency of state visitations, thereby providing an estimate for pseudo-counts for free. To scale this decomposition method to large-scale domains, we provide an algorithm that never requires building the transition matrix, can make use of deep networks, and also permits mini-batch training. Further, we draw inspiration from predictive state representations and extend our decomposition method to partially observable environments. With experiments on multi-task settings with partially observable domains, we show that the proposed method can not only learn useful representation on DM-Lab-30 environments (that have inputs involving language instructions, pixel images, and rewards, among others) but it can also be effective at hard exploration tasks in DM-Hard-8 environments.

Fast Rates for Maximum Entropy Exploration

We consider the reinforcement learning (RL) setting, in which the agent has to act in unknown environment driven by a Markov Decision Process (MDP) with sparse or even reward free signals. In this situation, exploration becomes the main challenge. In this work, we study the maximum entropy exploration problem of two different types. The first type is visitation entropy maximization that was previously considered by Hazan et al. (2019) in the discounted setting. For this type of exploration, we propose an algorithm based on a game theoretic representation that has $\widetilde{\mathcal{O}}(H^3 S^2 A / \varepsilon^2)$ sample complexity thus improving the $\varepsilon$-dependence of Hazan et al. (2019), where $S$ is a number of states, $A$ is a number of actions, $H$ is an episode length, and $\varepsilon$ is a desired accuracy. The second type of entropy we study is the trajectory entropy. This objective function is closely related to the entropy-regularized MDPs, and we propose a simple modification of the UCBVI algorithm that has a sample complexity of order $\widetilde{\mathcal{O}}(1/\varepsilon)$ ignoring dependence in $S, A, H$. Interestingly enough, it is the first theoretical result in RL literature establishing that the exploration problem for the regularized MDPs can be statistically strictly easier (in terms of sample complexity) than for the ordinary MDPs.

Optimistic Posterior Sampling for Reinforcement Learning with Few Samples and Tight Guarantees

We consider reinforcement learning in an environment modeled by an episodic, finite, stage-dependent Markov decision process of horizon $H$ with $S$ states, and $A$ actions. The performance of an agent is measured by the regret after interacting with the environment for $T$ episodes. We propose an optimistic posterior sampling algorithm for reinforcement learning (OPSRL), a simple variant of posterior sampling that only needs a number of posterior samples logarithmic in $H$, $S$, $A$, and $T$ per state-action pair. For OPSRL we guarantee a high-probability regret bound of order at most $\widetilde{\mathcal{O}}(\sqrt{H^3SAT})$ ignoring $\text{poly}\log(HSAT)$ terms. The key novel technical ingredient is a new sharp anti-concentration inequality for linear forms which may be of independent interest. Specifically, we extend the normal approximation-based lower bound for Beta distributions by Alfers and Dinges [1984] to Dirichlet distributions. Our bound matches the lower bound of order $\Omega(\sqrt{H^3SAT})$, thereby answering the open problems raised by Agrawal and Jia [2017b] for the episodic setting.

Mastering the Game of Stratego with Model-Free Multiagent Reinforcement Learning

We introduce DeepNash, an autonomous agent capable of learning to play the imperfect information game Stratego from scratch, up to a human expert level. Stratego is one of the few iconic board games that Artificial Intelligence (AI) has not yet mastered. This popular game has an enormous game tree on the order of $10^{535}$ nodes, i.e., $10^{175}$ times larger than that of Go. It has the additional complexity of requiring decision-making under imperfect information, similar to Texas hold'em poker, which has a significantly smaller game tree (on the order of $10^{164}$ nodes). Decisions in Stratego are made over a large number of discrete actions with no obvious link between action and outcome. Episodes are long, with often hundreds of moves before a player wins, and situations in Stratego can not easily be broken down into manageably-sized sub-problems as in poker. For these reasons, Stratego has been a grand challenge for the field of AI for decades, and existing AI methods barely reach an amateur level of play. DeepNash uses a game-theoretic, model-free deep reinforcement learning method, without search, that learns to master Stratego via self-play. The Regularised Nash Dynamics (R-NaD) algorithm, a key component of DeepNash, converges to an approximate Nash equilibrium, instead of 'cycling' around it, by directly modifying the underlying multi-agent learning dynamics. DeepNash beats existing state-of-the-art AI methods in Stratego and achieved a yearly (2022) and all-time top-3 rank on the Gravon games platform, competing with human expert players.

Game Plan: What AI can do for Football, and What Football can do for AI

The rapid progress in artificial intelligence (AI) and machine learning has opened unprecedented analytics possibilities in various team and individual sports, including baseball, basketball, and tennis. More recently, AI techniques have been applied to football, due to a huge increase in data collection by professional teams, increased computational power, and advances in machine learning, with the goal of better addressing new scientific challenges involved in the analysis of both individual players' and coordinated teams' behaviors. The research challenges associated with predictive and prescriptive football analytics require new developments and progress at the intersection of statistical learning, game theory, and computer vision. In this paper, we provide an overarching perspective highlighting how the combination of these fields, in particular, forms a unique microcosm for AI research, while offering mutual benefits for professional teams, spectators, and broadcasters in the years to come. We illustrate that this duality makes football analytics a game changer of tremendous value, in terms of not only changing the game of football itself, but also in terms of what this domain can mean for the field of AI. We review the state-of-the-art and exemplify the types of analysis enabled by combining the aforementioned fields, including illustrative examples of counterfactual analysis using predictive models, and the combination of game-theoretic analysis of penalty kicks with statistical learning of player attributes. We conclude by highlighting envisioned downstream impacts, including possibilities for extensions to other sports (real and virtual).

Navigating the Landscape of Games

Games are traditionally recognized as one of the key testbeds underlying progress in artificial intelligence (AI), aptly referred to as the "Drosophila of AI". Traditionally, researchers have focused on using games to build strong AI agents that, e.g., achieve human-level performance. This progress, however, also requires a classification of how 'interesting' a game is for an artificial agent. Tackling this latter question not only facilitates an understanding of the characteristics of learnt AI agents in games, but also helps to determine what game an AI should address next as part of its training. Here, we show how network measures applied to so-called response graphs of large-scale games enable the creation of a useful landscape of games, quantifying the relationships between games of widely varying sizes, characteristics, and complexities. We illustrate our findings in various domains, ranging from well-studied canonical games to significantly more complex empirical games capturing the performance of trained AI agents pitted against one another. Our results culminate in a demonstration of how one can leverage this information to automatically generate new and interesting games, including mixtures of empirical games synthesized from real world games.