Observation Noise and Initialization in Wide Neural Networks

Performing gradient descent in a wide neural network is equivalent to computing the posterior mean of a Gaussian Process with the Neural Tangent Kernel (NTK-GP), for a specific choice of prior mean and with zero observation noise. However, existing formulations of this result have two limitations: i) the resultant NTK-GP assumes no noise in the observed target variables, which can result in suboptimal predictions with noisy data; ii) it is unclear how to extend the equivalence to an arbitrary prior mean, a crucial aspect of formulating a well-specified model. To address the first limitation, we introduce a regularizer into the neural network's training objective, formally showing its correspondence to incorporating observation noise into the NTK-GP model. To address the second, we introduce a \textit{shifted network} that enables arbitrary prior mean functions. This approach allows us to perform gradient descent on a single neural network, without expensive ensembling or kernel matrix inversion. Our theoretical insights are validated empirically, with experiments exploring different values of observation noise and network architectures.

Impatient Bandits: Optimizing for the Long-Term Without Delay

Increasingly, recommender systems are tasked with improving users' long-term satisfaction. In this context, we study a content exploration task, which we formalize as a bandit problem with delayed rewards. There is an apparent trade-off in choosing the learning signal: waiting for the full reward to become available might take several weeks, slowing the rate of learning, whereas using short-term proxy rewards reflects the actual long-term goal only imperfectly. First, we develop a predictive model of delayed rewards that incorporates all information obtained to date. Rewards as well as shorter-term surrogate outcomes are combined through a Bayesian filter to obtain a probabilistic belief. Second, we devise a bandit algorithm that quickly learns to identify content aligned with long-term success using this new predictive model. We prove a regret bound for our algorithm that depends on the \textit{Value of Progressive Feedback}, an information theoretic metric that captures the quality of short-term leading indicators that are observed prior to the long-term reward. We apply our approach to a podcast recommendation problem, where we seek to recommend shows that users engage with repeatedly over two months. We empirically validate that our approach significantly outperforms methods that optimize for short-term proxies or rely solely on delayed rewards, as demonstrated by an A/B test in a recommendation system that serves hundreds of millions of users.

Epistemic Uncertainty and Observation Noise with the Neural Tangent Kernel

Recent work has shown that training wide neural networks with gradient descent is formally equivalent to computing the mean of the posterior distribution in a Gaussian Process (GP) with the Neural Tangent Kernel (NTK) as the prior covariance and zero aleatoric noise \parencite{jacot2018neural}. In this paper, we extend this framework in two ways. First, we show how to deal with non-zero aleatoric noise. Second, we derive an estimator for the posterior covariance, giving us a handle on epistemic uncertainty. Our proposed approach integrates seamlessly with standard training pipelines, as it involves training a small number of additional predictors using gradient descent on a mean squared error loss. We demonstrate the proof-of-concept of our method through empirical evaluation on synthetic regression.

On the Importance of Uncertainty in Decision-Making with Large Language Models

We investigate the role of uncertainty in decision-making problems with natural language as input. For such tasks, using Large Language Models as agents has become the norm. However, none of the recent approaches employ any additional phase for estimating the uncertainty the agent has about the world during the decision-making task. We focus on a fundamental decision-making framework with natural language as input, which is the one of contextual bandits, where the context information consists of text. As a representative of the approaches with no uncertainty estimation, we consider an LLM bandit with a greedy policy, which picks the action corresponding to the largest predicted reward. We compare this baseline to LLM bandits that make active use of uncertainty estimation by integrating the uncertainty in a Thompson Sampling policy. We employ different techniques for uncertainty estimation, such as Laplace Approximation, Dropout, and Epinets. We empirically show on real-world data that the greedy policy performs worse than the Thompson Sampling policies. These findings suggest that, while overlooked in the LLM literature, uncertainty plays a fundamental role in bandit tasks with LLMs.

Automatic Music Playlist Generation via Simulation-based Reinforcement Learning

Personalization of playlists is a common feature in music streaming services, but conventional techniques, such as collaborative filtering, rely on explicit assumptions regarding content quality to learn how to make recommendations. Such assumptions often result in misalignment between offline model objectives and online user satisfaction metrics. In this paper, we present a reinforcement learning framework that solves for such limitations by directly optimizing for user satisfaction metrics via the use of a simulated playlist-generation environment. Using this simulator we develop and train a modified Deep Q-Network, the action head DQN (AH-DQN), in a manner that addresses the challenges imposed by the large state and action space of our RL formulation. The resulting policy is capable of making recommendations from large and dynamic sets of candidate items with the expectation of maximizing consumption metrics. We analyze and evaluate agents offline via simulations that use environment models trained on both public and proprietary streaming datasets. We show how these agents lead to better user-satisfaction metrics compared to baseline methods during online A/B tests. Finally, we demonstrate that performance assessments produced from our simulator are strongly correlated with observed online metric results.

Impatient Bandits: Optimizing Recommendations for the Long-Term Without Delay

Recommender systems are a ubiquitous feature of online platforms. Increasingly, they are explicitly tasked with increasing users' long-term satisfaction. In this context, we study a content exploration task, which we formalize as a multi-armed bandit problem with delayed rewards. We observe that there is an apparent trade-off in choosing the learning signal: Waiting for the full reward to become available might take several weeks, hurting the rate at which learning happens, whereas measuring short-term proxy rewards reflects the actual long-term goal only imperfectly. We address this challenge in two steps. First, we develop a predictive model of delayed rewards that incorporates all information obtained to date. Full observations as well as partial (short or medium-term) outcomes are combined through a Bayesian filter to obtain a probabilistic belief. Second, we devise a bandit algorithm that takes advantage of this new predictive model. The algorithm quickly learns to identify content aligned with long-term success by carefully balancing exploration and exploitation. We apply our approach to a podcast recommendation problem, where we seek to identify shows that users engage with repeatedly over two months. We empirically validate that our approach results in substantially better performance compared to approaches that either optimize for short-term proxies, or wait for the long-term outcome to be fully realized.

A Strong Baseline for Batch Imitation Learning

Imitation of expert behaviour is a highly desirable and safe approach to the problem of sequential decision making. We provide an easy-to-implement, novel algorithm for imitation learning under a strict data paradigm, in which the agent must learn solely from data collected a priori. This paradigm allows our algorithm to be used for environments in which safety or cost are of critical concern. Our algorithm requires no additional hyper-parameter tuning beyond any standard batch reinforcement learning (RL) algorithm, making it an ideal baseline for such data-strict regimes. Furthermore, we provide formal sample complexity guarantees for the algorithm in finite Markov Decision Problems. In doing so, we formally demonstrate an unproven claim from Kearns & Singh (1998). On the empirical side, our contribution is twofold. First, we develop a practical, robust and principled evaluation protocol for offline RL methods, making use of only the dataset provided for model selection. This stands in contrast to the vast majority of previous works in offline RL, which tune hyperparameters on the evaluation environment, limiting the practical applicability when deployed in new, cost-critical environments. As such, we establish precedent for the development and fair evaluation of offline RL algorithms. Second, we evaluate our own algorithm on challenging continuous control benchmarks, demonstrating its practical applicability and competitiveness with state-of-the-art performance, despite being a simpler algorithm.

Imitation Learning by Reinforcement Learning

Imitation Learning algorithms learn a policy from demonstrations of expert behavior. Somewhat counterintuitively, we show that, for deterministic experts, imitation learning can be done by reduction to reinforcement learning, which is commonly considered more difficult. We conduct experiments which confirm that our reduction works well in practice for a continuous control task.

Information Directed Reward Learning for Reinforcement Learning

For many reinforcement learning (RL) applications, specifying a reward is difficult. In this paper, we consider an RL setting where the agent can obtain information about the reward only by querying an expert that can, for example, evaluate individual states or provide binary preferences over trajectories. From such expensive feedback, we aim to learn a model of the reward function that allows standard RL algorithms to achieve high expected return with as few expert queries as possible. For this purpose, we propose Information Directed Reward Learning (IDRL), which uses a Bayesian model of the reward function and selects queries that maximize the information gain about the difference in return between potentially optimal policies. In contrast to prior active reward learning methods designed for specific types of queries, IDRL naturally accommodates different query types. Moreover, by shifting the focus from reducing the reward approximation error to improving the policy induced by the reward model, it achieves similar or better performance with significantly fewer queries. We support our findings with extensive evaluations in multiple environments and with different types of queries.

Estimating $α$-Rank by Maximizing Information Gain

Game theory has been increasingly applied in settings where the game is not known outright, but has to be estimated by sampling. For example, meta-games that arise in multi-agent evaluation can only be accessed by running a succession of expensive experiments that may involve simultaneous deployment of several agents. In this paper, we focus on $\alpha$-rank, a popular game-theoretic solution concept designed to perform well in such scenarios. We aim to estimate the $\alpha$-rank of the game using as few samples as possible. Our algorithm maximizes information gain between an epistemic belief over the $\alpha$-ranks and the observed payoff. This approach has two main benefits. First, it allows us to focus our sampling on the entries that matter the most for identifying the $\alpha$-rank. Second, the Bayesian formulation provides a facility to build in modeling assumptions by using a prior over game payoffs. We show the benefits of using information gain as compared to the confidence interval criterion of ResponseGraphUCB (Rowland et al. 2019), and provide theoretical results justifying our method.