Zheng Wen

Akhil Agnihotri, Rahul Jain, Deepak Ramachandran et al.

Post-training LLMs with RLHF and preference optimization methods (e.g., DPO, IPO) has greatly improved alignment, yet these approaches assume a single objective. In reality, humans express multiple, often conflicting objectives, such as helpfulness and harmlessness, with no natural scalarization. We study the multi-objective preference alignment problem, where a policy must balance several objectives simultaneously. We propose Multi-Objective Preference Optimization (MOPO), a constrained KL-regularized framework that maximizes a primary objective while enforcing lower bounds on secondary objectives via tunable safety thresholds. MOPO operates directly on pairwise preferences without point-wise rewards, and admits simple closed-form iterative updates. Empirically, MOPO recovers Pareto-optimal policies on synthetic benchmarks and, when fine-tuned on human-preference data, yields multi-billion parameter models that achieve higher rewards and Pareto-dominate baselines, with stable and robust optimization dynamics.

Dengwang Tang, Rahul Jain, Botao Hao et al.

In this paper, we study the problem of efficient online reinforcement learning in the infinite horizon setting when there is an offline dataset to start with. We assume that the offline dataset is generated by an expert but with unknown level of competence, i.e., it is not perfect and not necessarily using the optimal policy. We show that if the learning agent models the behavioral policy (parameterized by a competence parameter) used by the expert, it can do substantially better in terms of minimizing cumulative regret, than if it doesn't do that. We establish an upper bound on regret of the exact informed PSRL algorithm that scales as $\tilde{O}(\sqrt{T})$. This requires a novel prior-dependent regret analysis of Bayesian online learning algorithms for the infinite horizon setting. We then propose the Informed RLSVI algorithm to efficiently approximate the iPSRL algorithm.

Akhil Agnihotri, Rahul Jain, Deepak Ramachandran et al.

Reinforcement Learning from Human Feedback (RLHF) has emerged as a powerful approach for aligning generative models, but its reliance on learned reward models makes it vulnerable to mis-specification and reward hacking. Preference-based Reinforcement Learning (PbRL) offers a more robust alternative by directly leveraging noisy binary comparisons over trajectories. We study the best policy identification problem in PbRL, motivated by post-training optimization of generative models, for example, during multi-turn interactions. Learning in this setting combines an offline preference dataset--potentially biased or out-of-distribution and collected from a rater of subpar 'competence'--with online pure exploration, making systematic online learning essential. To this end, we propose Posterior Sampling for Preference Learning ($\mathsf{PSPL}$), a novel algorithm inspired by Top-Two Thompson Sampling that maintains posteriors over the reward model and dynamics. We provide the first Bayesian simple regret guarantees for PbRL and introduce an efficient approximation that outperforms existing baselines on simulation and image generation benchmarks.

Akhil Agnihotri, Rahul Jain, Deepak Ramachandran et al.

Reinforcement Learning with Human Feedback (RLHF) is at the core of fine-tuning methods for generative AI models for language and images. Such feedback is often sought as rank or preference feedback from human raters, as opposed to eliciting scores since the latter tends to be noisy. On the other hand, RL theory and algorithms predominantly assume that a reward feedback is available. In particular, approaches for online learning that can be helpful in adaptive data collection via active learning cannot incorporate offline preference data. In this paper, we adopt a finite-armed linear bandit model as a prototypical model of online learning. We consider an offline preference dataset to be available generated by an expert of unknown 'competence'. We propose warmPref-PS, a posterior sampling algorithm for online learning that can be warm-started with an offline dataset with noisy preference feedback. We show that by modeling the 'competence' of the expert that generated it, we are able to use such a dataset most effectively. We support our claims with novel theoretical analysis of its Bayesian regret, as well as, extensive empirical evaluation of an approximate loss function that optimizes for infinitely many arms, and performs substantially better than baselines.

Ian Osband, Zheng Wen, Seyed Mohammad Asghari et al.

Intelligence relies on an agent's knowledge of what it does not know. This capability can be assessed based on the quality of joint predictions of labels across multiple inputs. In principle, ensemble-based approaches produce effective joint predictions, but the computational costs of training large ensembles can become prohibitive. We introduce the epinet: an architecture that can supplement any conventional neural network, including large pretrained models, and can be trained with modest incremental computation to estimate uncertainty. With an epinet, conventional neural networks outperform very large ensembles, consisting of hundreds or more particles, with orders of magnitude less computation. The epinet does not fit the traditional framework of Bayesian neural networks. To accommodate development of approaches beyond BNNs, such as the epinet, we introduce the epistemic neural network (ENN) as an interface for models that produce joint predictions.

Alfonso Lobos, Paul Grigas, Zheng Wen

We consider an online revenue maximization problem over a finite time horizon subject to lower and upper bounds on cost. At each period, an agent receives a context vector sampled i.i.d. from an unknown distribution and needs to make a decision adaptively. The revenue and cost functions depend on the context vector as well as some fixed but possibly unknown parameter vector to be learned. We propose a novel offline benchmark and a new algorithm that mixes an online dual mirror descent scheme with a generic parameter learning process. When the parameter vector is known, we demonstrate an $O(\sqrt{T})$ regret result as well an $O(\sqrt{T})$ bound on the possible constraint violations. When the parameter is not known and must be learned, we demonstrate that the regret and constraint violations are the sums of the previous $O(\sqrt{T})$ terms plus terms that directly depend on the convergence of the learning process.

Xiuyuan Lu, Benjamin Van Roy, Vikranth Dwaracherla et al.

Reinforcement learning agents have demonstrated remarkable achievements in simulated environments. Data efficiency poses an impediment to carrying this success over to real environments. The design of data-efficient agents calls for a deeper understanding of information acquisition and representation. We discuss concepts and regret analysis that together offer principled guidance. This line of thinking sheds light on questions of what information to seek, how to seek that information, and what information to retain. To illustrate concepts, we design simple agents that build on them and present computational results that highlight data efficiency.

Pan Xu, Zheng Wen, Handong Zhao et al.

We study a general class of contextual bandits, where each context-action pair is associated with a raw feature vector, but the reward generating function is unknown. We propose a novel learning algorithm that transforms the raw feature vector using the last hidden layer of a deep ReLU neural network (deep representation learning), and uses an upper confidence bound (UCB) approach to explore in the last linear layer (shallow exploration). We prove that under standard assumptions, our proposed algorithm achieves $\tilde{O}(\sqrt{T})$ finite-time regret, where $T$ is the learning time horizon. Compared with existing neural contextual bandit algorithms, our approach is computationally much more efficient since it only needs to explore in the last layer of the deep neural network.

Jing Shi, Ning Xu, Trung Bui et al.

Language-driven image editing can significantly save the laborious image editing work and be friendly to the photography novice. However, most similar work can only deal with a specific image domain or can only do global retouching. To solve this new task, we first present a new language-driven image editing dataset that supports both local and global editing with editing operation and mask annotations. Besides, we also propose a baseline method that fully utilizes the annotation to solve this problem. Our new method treats each editing operation as a sub-module and can automatically predict operation parameters. Not only performing well on challenging user data, but such an approach is also highly interpretable. We believe our work, including both the benchmark and the baseline, will advance the image editing area towards a more general and free-form level.

Wenlong Mou, Zheng Wen, Xi Chen

We study the optimal sample complexity in large-scale Reinforcement Learning (RL) problems with policy space generalization, i.e. the agent has a prior knowledge that the optimal policy lies in a known policy space. Existing results show that without a generalization model, the sample complexity of an RL algorithm will inevitably depend on the cardinalities of state space and action space, which are intractably large in many practical problems. To avoid such undesirable dependence on the state and action space sizes, this paper proposes a new notion of eluder dimension for the policy space, which characterizes the intrinsic complexity of policy learning in an arbitrary Markov Decision Process (MDP). Using a simulator oracle, we prove a near-optimal sample complexity upper bound that only depends linearly on the eluder dimension. We further prove a similar regret bound in deterministic systems without the simulator.

Youngsuk Park, Ryan A. Rossi, Zheng Wen et al.

Linear quadratic regulator (LQR) is one of the most popular frameworks to tackle continuous Markov decision process tasks. With its fundamental theory and tractable optimal policy, LQR has been revisited and analyzed in recent years, in terms of reinforcement learning scenarios such as the model-free or model-based setting. In this paper, we introduce the \textit{Structured Policy Iteration} (S-PI) for LQR, a method capable of deriving a structured linear policy. Such a structured policy with (block) sparsity or low-rank can have significant advantages over the standard LQR policy: more interpretable, memory-efficient, and well-suited for the distributed setting. In order to derive such a policy, we first cast a regularized LQR problem when the model is known. Then, our Structured Policy Iteration (S-PI) algorithm, which takes a policy evaluation step and a policy improvement step in an iterative manner, can solve this regularized LQR efficiently. We further extend the S-PI algorithm to the model-free setting where a smoothing procedure is adopted to estimate the gradient. In both the known-model and model-free setting, we prove convergence analysis under the proper choice of parameters. Finally, the experiments demonstrate the advantages of S-PI in terms of balancing the LQR performance and level of structure by varying the weight parameter.

Tong Yu, Branislav Kveton, Zheng Wen et al.

We propose a novel framework for structured bandits, which we call an influence diagram bandit. Our framework captures complex statistical dependencies between actions, latent variables, and observations; and thus unifies and extends many existing models, such as combinatorial semi-bandits, cascading bandits, and low-rank bandits. We develop novel online learning algorithms that learn to act efficiently in our models. The key idea is to track a structured posterior distribution of model parameters, either exactly or approximately. To act, we sample model parameters from their posterior and then use the structure of the influence diagram to find the most optimistic action under the sampled parameters. We empirically evaluate our algorithms in three structured bandit problems, and show that they perform as well as or better than problem-specific state-of-the-art baselines.

Vikranth Dwaracherla, Xiuyuan Lu, Morteza Ibrahimi et al.

We study the use of hypermodels to represent epistemic uncertainty and guide exploration. This generalizes and extends the use of ensembles to approximate Thompson sampling. The computational cost of training an ensemble grows with its size, and as such, prior work has typically been limited to ensembles with tens of elements. We show that alternative hypermodels can enjoy dramatic efficiency gains, enabling behavior that would otherwise require hundreds or thousands of elements, and even succeed in situations where ensemble methods fail to learn regardless of size. This allows more accurate approximation of Thompson sampling as well as use of more sophisticated exploration schemes. In particular, we consider an approximate form of information-directed sampling and demonstrate performance gains relative to Thompson sampling. As alternatives to ensembles, we consider linear and neural network hypermodels, also known as hypernetworks. We prove that, with neural network base models, a linear hypermodel can represent essentially any distribution over functions, and as such, hypernetworks are no more expressive.

Ruiyi Zhang, Changyou Chen, Zhe Gan et al.

Auto-regressive text generation models usually focus on local fluency, and may cause inconsistent semantic meaning in long text generation. Further, automatically generating words with similar semantics is challenging, and hand-crafted linguistic rules are difficult to apply. We consider a text planning scheme and present a model-based imitation-learning approach to alleviate the aforementioned issues. Specifically, we propose a novel guider network to focus on the generative process over a longer horizon, which can assist next-word prediction and provide intermediate rewards for generator optimization. Extensive experiments demonstrate that the proposed method leads to improved performance.

Ruiyi Zhang, Changyou Chen, Zhe Gan et al.

Reinforcement learning (RL) has been widely studied for improving sequence-generation models. However, the conventional rewards used for RL training typically cannot capture sufficient semantic information and therefore render model bias. Further, the sparse and delayed rewards make RL exploration inefficient. To alleviate these issues, we propose the concept of nested-Wasserstein distance for distributional semantic matching. To further exploit it, a novel nested-Wasserstein self-imitation learning framework is developed, encouraging the model to exploit historical high-rewarded sequences for enhanced exploration and better semantic matching. Our solution can be understood as approximately executing proximal policy optimization with Wasserstein trust-regions. Experiments on a variety of unconditional and conditional sequence-generation tasks demonstrate the proposed approach consistently leads to improved performance.

Botao Hao, Yasin Abbasi-Yadkori, Zheng Wen et al.

Upper Confidence Bound (UCB) method is arguably the most celebrated one used in online decision making with partial information feedback. Existing techniques for constructing confidence bounds are typically built upon various concentration inequalities, which thus lead to over-exploration. In this paper, we propose a non-parametric and data-dependent UCB algorithm based on the multiplier bootstrap. To improve its finite sample performance, we further incorporate second-order correction into the above construction. In theory, we derive both problem-dependent and problem-independent regret bounds for multi-armed bandits under a much weaker tail assumption than the standard sub-Gaussianity. Numerical results demonstrate significant regret reductions by our method, in comparison with several baselines in a range of multi-armed and linear bandit problems.

Branislav Kveton, Saied Mahdian, S. Muthukrishnan et al.

A popular approach to selling online advertising is by a waterfall, where a publisher makes sequential price offers to ad networks for an inventory, and chooses the winner in that order. The publisher picks the order and prices to maximize her revenue. A traditional solution is to learn the demand model and then subsequently solve the optimization problem for the given demand model. This will incur a linear regret. We design an online learning algorithm for solving this problem, which interleaves learning and optimization, and prove that this algorithm has sublinear regret. We evaluate the algorithm on both synthetic and real-world data, and show that it quickly learns high quality pricing strategies. This is the first principled study of learning a waterfall design online by sequential experimentation.

Shuai Li, Wei Chen, Zheng Wen et al.

We consider a problem of stochastic online learning with general probabilistic graph feedback, where each directed edge in the feedback graph has probability $p_{ij}$. Two cases are covered. (a) The one-step case, where after playing arm $i$ the learner observes a sample reward feedback of arm $j$ with independent probability $p_{ij}$. (b) The cascade case where after playing arm $i$ the learner observes feedback of all arms $j$ in a probabilistic cascade starting from $i$ -- for each $(i,j)$ with probability $p_{ij}$, if arm $i$ is played or observed, then a reward sample of arm $j$ would be observed with independent probability $p_{ij}$. Previous works mainly focus on deterministic graphs which corresponds to one-step case with $p_{ij} \in \{0,1\}$, an adversarial sequence of graphs with certain topology guarantees, or a specific type of random graphs. We analyze the asymptotic lower bounds and design algorithms in both cases. The regret upper bounds of the algorithms match the lower bounds with high probability.

Ruiyi Zhang, Zheng Wen, Changyou Chen et al.

Thompson sampling (TS) is a class of algorithms for sequential decision-making, which requires maintaining a posterior distribution over a model. However, calculating exact posterior distributions is intractable for all but the simplest models. Consequently, efficient computation of an approximate posterior distribution is a crucial problem for scalable TS with complex models, such as neural networks. In this paper, we use distribution optimization techniques to approximate the posterior distribution, solved via Wasserstein gradient flows. Based on the framework, a principled particle-optimization algorithm is developed for TS to approximate the posterior efficiently. Our approach is scalable and does not make explicit distribution assumptions on posterior approximations. Extensive experiments on both synthetic data and real large-scale data demonstrate the superior performance of the proposed methods.

Branislav Kveton, Csaba Szepesvari, Sharan Vaswani et al.

We propose a bandit algorithm that explores by randomizing its history of rewards. Specifically, it pulls the arm with the highest mean reward in a non-parametric bootstrap sample of its history with pseudo rewards. We design the pseudo rewards such that the bootstrap mean is optimistic with a sufficiently high probability. We call our algorithm Giro, which stands for garbage in, reward out. We analyze Giro in a Bernoulli bandit and derive a $O(K Δ^{-1} \log n)$ bound on its $n$-round regret, where $Δ$ is the difference in the expected rewards of the optimal and the best suboptimal arms, and $K$ is the number of arms. The main advantage of our exploration design is that it easily generalizes to structured problems. To show this, we propose contextual Giro with an arbitrary reward generalization model. We evaluate Giro and its contextual variant on multiple synthetic and real-world problems, and observe that it performs well.

Prakhar Gupta, Gaurush Hiranandani, Harvineet Singh et al.

Learning to rank is an important problem in machine learning and recommender systems. In a recommender system, a user is typically recommended a list of items. Since the user is unlikely to examine the entire recommended list, partial feedback arises naturally. At the same time, diverse recommendations are important because it is challenging to model all tastes of the user in practice. In this paper, we propose the first algorithm for online learning to rank diverse items from partial-click feedback. We assume that the user examines the list of recommended items until the user is attracted by an item, which is clicked, and does not examine the rest of the items. This model of user behavior is known as the cascade model. We propose an online learning algorithm, cascadelsb, for solving our problem. The algorithm actively explores the tastes of the user with the objective of learning to recommend the optimal diverse list. We analyze the algorithm and prove a gap-free upper bound on its n-step regret. We evaluate cascadelsb on both synthetic and real-world datasets, compare it to various baselines, and show that it learns even when our modeling assumptions do not hold exactly.

Sumeet Katariya, Branislav Kveton, Zheng Wen et al.

In many practical problems, a learning agent may want to learn the best action in hindsight without ever taking a bad action, which is significantly worse than the default production action. In general, this is impossible because the agent has to explore unknown actions, some of which can be bad, to learn better actions. However, when the actions are combinatorial, this may be possible if the unknown action can be evaluated by interleaving it with the production action. We formalize this concept as learning in stochastic combinatorial semi-bandits with exchangeable actions. We design efficient learning algorithms for this problem, bound their n-step regret, and evaluate them on both synthetic and real-world problems. Our real-world experiments show that our algorithms can learn to recommend K most attractive movies without ever violating a strict production constraint, both overall and subject to a diversity constraint.

Sharan Vaswani, Branislav Kveton, Zheng Wen et al.

We investigate the use of bootstrapping in the bandit setting. We first show that the commonly used non-parametric bootstrapping (NPB) procedure can be provably inefficient and establish a near-linear lower bound on the regret incurred by it under the bandit model with Bernoulli rewards. We show that NPB with an appropriate amount of forced exploration can result in sub-linear albeit sub-optimal regret. As an alternative to NPB, we propose a weighted bootstrapping (WB) procedure. For Bernoulli rewards, WB with multiplicative exponential weights is mathematically equivalent to Thompson sampling (TS) and results in near-optimal regret bounds. Similarly, in the bandit setting with Gaussian rewards, we show that WB with additive Gaussian weights achieves near-optimal regret. Beyond these special cases, we show that WB leads to better empirical performance than TS for several reward distributions bounded on $[0,1]$. For the contextual bandit setting, we give practical guidelines that make bootstrapping simple and efficient to implement and result in good empirical performance on real-world datasets.

Yang Cao, Zheng Wen, Branislav Kveton et al.

Multi-armed bandit (MAB) is a class of online learning problems where a learning agent aims to maximize its expected cumulative reward while repeatedly selecting to pull arms with unknown reward distributions. We consider a scenario where the reward distributions may change in a piecewise-stationary fashion at unknown time steps. We show that by incorporating a simple change-detection component with classic UCB algorithms to detect and adapt to changes, our so-called M-UCB algorithm can achieve nearly optimal regret bound on the order of $O(\sqrt{MKT\log T})$, where $T$ is the number of time steps, $K$ is the number of arms, and $M$ is the number of stationary segments. Comparison with the best available lower bound shows that our M-UCB is nearly optimal in $T$ up to a logarithmic factor. We also compare M-UCB with the state-of-the-art algorithms in numerical experiments using a public Yahoo! dataset to demonstrate its superior performance.

Branislav Kveton, Csaba Szepesvari, Anup Rao et al.

Many problems in computer vision and recommender systems involve low-rank matrices. In this work, we study the problem of finding the maximum entry of a stochastic low-rank matrix from sequential observations. At each step, a learning agent chooses pairs of row and column arms, and receives the noisy product of their latent values as a reward. The main challenge is that the latent values are unobserved. We identify a class of non-negative matrices whose maximum entry can be found statistically efficiently and propose an algorithm for finding them, which we call LowRankElim. We derive a $\DeclareMathOperator{\poly}{poly} O((K + L) \poly(d) Δ^{-1} \log n)$ upper bound on its $n$-step regret, where $K$ is the number of rows, $L$ is the number of columns, $d$ is the rank of the matrix, and $Δ$ is the minimum gap. The bound depends on other problem-specific constants that clearly do not depend $K L$. To the best of our knowledge, this is the first such result in the literature.

Georgios Theocharous, Zheng Wen, Yasin Abbasi-Yadkori et al.

We propose a practical non-episodic PSRL algorithm that unlike recent state-of-the-art PSRL algorithms uses a deterministic, model-independent episode switching schedule. Our algorithm termed deterministic schedule PSRL (DS-PSRL) is efficient in terms of time, sample, and space complexity. We prove a Bayesian regret bound under mild assumptions. Our result is more generally applicable to multiple parameters and continuous state action problems. We compare our algorithm with state-of-the-art PSRL algorithms on standard discrete and continuous problems from the literature. Finally, we show how the assumptions of our algorithm satisfy a sensible parametrization for a large class of problems in sequential recommendations.

Daniel Russo, Benjamin Van Roy, Abbas Kazerouni et al.

Thompson sampling is an algorithm for online decision problems where actions are taken sequentially in a manner that must balance between exploiting what is known to maximize immediate performance and investing to accumulate new information that may improve future performance. The algorithm addresses a broad range of problems in a computationally efficient manner and is therefore enjoying wide use. This tutorial covers the algorithm and its application, illustrating concepts through a range of examples, including Bernoulli bandit problems, shortest path problems, product recommendation, assortment, active learning with neural networks, and reinforcement learning in Markov decision processes. Most of these problems involve complex information structures, where information revealed by taking an action informs beliefs about other actions. We will also discuss when and why Thompson sampling is or is not effective and relations to alternative algorithms.

Ian Osband, Benjamin Van Roy, Daniel Russo et al.

We study the use of randomized value functions to guide deep exploration in reinforcement learning. This offers an elegant means for synthesizing statistically and computationally efficient exploration with common practical approaches to value function learning. We present several reinforcement learning algorithms that leverage randomized value functions and demonstrate their efficacy through computational studies. We also prove a regret bound that establishes statistical efficiency with a tabular representation.

Sumeet Katariya, Branislav Kveton, Csaba Szepesvári et al.

The probability that a user will click a search result depends both on its relevance and its position on the results page. The position based model explains this behavior by ascribing to every item an attraction probability, and to every position an examination probability. To be clicked, a result must be both attractive and examined. The probabilities of an item-position pair being clicked thus form the entries of a rank-$1$ matrix. We propose the learning problem of a Bernoulli rank-$1$ bandit where at each step, the learning agent chooses a pair of row and column arms, and receives the product of their Bernoulli-distributed values as a reward. This is a special case of the stochastic rank-$1$ bandit problem considered in recent work that proposed an elimination based algorithm Rank1Elim, and showed that Rank1Elim's regret scales linearly with the number of rows and columns on "benign" instances. These are the instances where the minimum of the average row and column rewards $μ$ is bounded away from zero. The issue with Rank1Elim is that it fails to be competitive with straightforward bandit strategies as $μ\rightarrow 0$. In this paper we propose Rank1ElimKL which simply replaces the (crude) confidence intervals of Rank1Elim with confidence intervals based on Kullback-Leibler (KL) divergences, and with the help of a novel result concerning the scaling of KL divergences we prove that with this change, our algorithm will be competitive no matter the value of $μ$. Experiments with synthetic data confirm that on benign instances the performance of Rank1ElimKL is significantly better than that of even Rank1Elim, while experiments with models derived from real data confirm that the improvements are significant across the board, regardless of whether the data is benign or not.

Masrour Zoghi, Tomas Tunys, Mohammad Ghavamzadeh et al.

Online learning to rank is a core problem in information retrieval and machine learning. Many provably efficient algorithms have been recently proposed for this problem in specific click models. The click model is a model of how the user interacts with a list of documents. Though these results are significant, their impact on practice is limited, because all proposed algorithms are designed for specific click models and lack convergence guarantees in other models. In this work, we propose BatchRank, the first online learning to rank algorithm for a broad class of click models. The class encompasses two most fundamental click models, the cascade and position-based models. We derive a gap-dependent upper bound on the $T$-step regret of BatchRank and evaluate it on a range of web search queries. We observe that BatchRank outperforms ranked bandits and is more robust than CascadeKL-UCB, an existing algorithm for the cascade model.

Sharan Vaswani, Branislav Kveton, Zheng Wen et al.

We consider influence maximization (IM) in social networks, which is the problem of maximizing the number of users that become aware of a product by selecting a set of "seed" users to expose the product to. While prior work assumes a known model of information diffusion, we propose a novel parametrization that not only makes our framework agnostic to the underlying diffusion model, but also statistically efficient to learn from data. We give a corresponding monotone, submodular surrogate function, and show that it is a good approximation to the original IM objective. We also consider the case of a new marketer looking to exploit an existing social network, while simultaneously learning the factors governing information propagation. For this, we propose a pairwise-influence semi-bandit feedback model and develop a LinUCB-based bandit algorithm. Our model-independent analysis shows that our regret bound has a better (as compared to previous work) dependence on the size of the network. Experimental evaluation suggests that our framework is robust to the underlying diffusion model and can efficiently learn a near-optimal solution.

Sumeet Katariya, Branislav Kveton, Csaba Szepesvari et al.

We propose stochastic rank-$1$ bandits, a class of online learning problems where at each step a learning agent chooses a pair of row and column arms, and receives the product of their values as a reward. The main challenge of the problem is that the individual values of the row and column are unobserved. We assume that these values are stochastic and drawn independently. We propose a computationally-efficient algorithm for solving our problem, which we call Rank1Elim. We derive a $O((K + L) (1 / Δ) \log n)$ upper bound on its $n$-step regret, where $K$ is the number of rows, $L$ is the number of columns, and $Δ$ is the minimum of the row and column gaps; under the assumption that the mean row and column rewards are bounded away from zero. To the best of our knowledge, we present the first bandit algorithm that finds the maximum entry of a rank-$1$ matrix whose regret is linear in $K + L$, $1 / Δ$, and $\log n$. We also derive a nearly matching lower bound. Finally, we evaluate Rank1Elim empirically on multiple problems. We observe that it leverages the structure of our problems and can learn near-optimal solutions even if our modeling assumptions are mildly violated.

Shi Zong, Hao Ni, Kenny Sung et al.

Most recommender systems recommend a list of items. The user examines the list, from the first item to the last, and often chooses the first attractive item and does not examine the rest. This type of user behavior can be modeled by the cascade model. In this work, we study cascading bandits, an online learning variant of the cascade model where the goal is to recommend $K$ most attractive items from a large set of $L$ candidate items. We propose two algorithms for solving this problem, which are based on the idea of linear generalization. The key idea in our solutions is that we learn a predictor of the attraction probabilities of items from their features, as opposing to learning the attraction probability of each item independently as in the existing work. This results in practical learning algorithms whose regret does not depend on the number of items $L$. We bound the regret of one algorithm and comprehensively evaluate the other on a range of recommendation problems. The algorithm performs well and outperforms all baselines.

Branislav Kveton, Zheng Wen, Azin Ashkan et al.

We propose combinatorial cascading bandits, a class of partial monitoring problems where at each step a learning agent chooses a tuple of ground items subject to constraints and receives a reward if and only if the weights of all chosen items are one. The weights of the items are binary, stochastic, and drawn independently of each other. The agent observes the index of the first chosen item whose weight is zero. This observation model arises in network routing, for instance, where the learning agent may only observe the first link in the routing path which is down, and blocks the path. We propose a UCB-like algorithm for solving our problems, CombCascade; and prove gap-dependent and gap-free upper bounds on its $n$-step regret. Our proofs build on recent work in stochastic combinatorial semi-bandits but also address two novel challenges of our setting, a non-linear reward function and partial observability. We evaluate CombCascade on two real-world problems and show that it performs well even when our modeling assumptions are violated. We also demonstrate that our setting requires a new learning algorithm.

Branislav Kveton, Csaba Szepesvari, Zheng Wen et al.

A search engine usually outputs a list of $K$ web pages. The user examines this list, from the first web page to the last, and chooses the first attractive page. This model of user behavior is known as the cascade model. In this paper, we propose cascading bandits, a learning variant of the cascade model where the objective is to identify $K$ most attractive items. We formulate our problem as a stochastic combinatorial partial monitoring problem. We propose two algorithms for solving it, CascadeUCB1 and CascadeKL-UCB. We also prove gap-dependent upper bounds on the regret of these algorithms and derive a lower bound on the regret in cascading bandits. The lower bound matches the upper bound of CascadeKL-UCB up to a logarithmic factor. We experiment with our algorithms on several problems. The algorithms perform surprisingly well even when our modeling assumptions are violated.

Branislav Kveton, Zheng Wen, Azin Ashkan et al.

A stochastic combinatorial semi-bandit is an online learning problem where at each step a learning agent chooses a subset of ground items subject to constraints, and then observes stochastic weights of these items and receives their sum as a payoff. In this paper, we close the problem of computationally and sample efficient learning in stochastic combinatorial semi-bandits. In particular, we analyze a UCB-like algorithm for solving the problem, which is known to be computationally efficient; and prove $O(K L (1 / Δ) \log n)$ and $O(\sqrt{K L n \log n})$ upper bounds on its $n$-step regret, where $L$ is the number of ground items, $K$ is the maximum number of chosen items, and $Δ$ is the gap between the expected returns of the optimal and best suboptimal solutions. The gap-dependent bound is tight up to a constant factor and the gap-free bound is tight up to a polylogarithmic factor.

Zheng Wen, Branislav Kveton, Azin Ashkan

A stochastic combinatorial semi-bandit is an online learning problem where at each step a learning agent chooses a subset of ground items subject to combinatorial constraints, and then observes stochastic weights of these items and receives their sum as a payoff. In this paper, we consider efficient learning in large-scale combinatorial semi-bandits with linear generalization, and as a solution, propose two learning algorithms called Combinatorial Linear Thompson Sampling (CombLinTS) and Combinatorial Linear UCB (CombLinUCB). Both algorithms are computationally efficient as long as the offline version of the combinatorial problem can be solved efficiently. We establish that CombLinTS and CombLinUCB are also provably statistically efficient under reasonable assumptions, by developing regret bounds that are independent of the problem scale (number of items) and sublinear in time. We also evaluate CombLinTS on a variety of problems with thousands of items. Our experiment results demonstrate that CombLinTS is scalable, robust to the choice of algorithm parameters, and significantly outperforms the best of our baselines.

Branislav Kveton, Zheng Wen, Azin Ashkan et al.

Many important optimization problems, such as the minimum spanning tree and minimum-cost flow, can be solved optimally by a greedy method. In this work, we study a learning variant of these problems, where the model of the problem is unknown and has to be learned by interacting repeatedly with the environment in the bandit setting. We formalize our learning problem quite generally, as learning how to maximize an unknown modular function on a known polymatroid. We propose a computationally efficient algorithm for solving our problem and bound its expected cumulative regret. Our gap-dependent upper bound is tight up to a constant and our gap-free upper bound is tight up to polylogarithmic factors. Finally, we evaluate our method on three problems and demonstrate that it is practical.

Branislav Kveton, Zheng Wen, Azin Ashkan et al.

A matroid is a notion of independence in combinatorial optimization which is closely related to computational efficiency. In particular, it is well known that the maximum of a constrained modular function can be found greedily if and only if the constraints are associated with a matroid. In this paper, we bring together the ideas of bandits and matroids, and propose a new class of combinatorial bandits, matroid bandits. The objective in these problems is to learn how to maximize a modular function on a matroid. This function is stochastic and initially unknown. We propose a practical algorithm for solving our problem, Optimistic Matroid Maximization (OMM); and prove two upper bounds, gap-dependent and gap-free, on its regret. Both bounds are sublinear in time and at most linear in all other quantities of interest. The gap-dependent upper bound is tight and we prove a matching lower bound on a partition matroid bandit. Finally, we evaluate our method on three real-world problems and show that it is practical.

Ian Osband, Benjamin Van Roy, Zheng Wen

We propose randomized least-squares value iteration (RLSVI) -- a new reinforcement learning algorithm designed to explore and generalize efficiently via linearly parameterized value functions. We explain why versions of least-squares value iteration that use Boltzmann or epsilon-greedy exploration can be highly inefficient, and we present computational results that demonstrate dramatic efficiency gains enjoyed by RLSVI. Further, we establish an upper bound on the expected regret of RLSVI that demonstrates near-optimality in a tabula rasa learning context. More broadly, our results suggest that randomized value functions offer a promising approach to tackling a critical challenge in reinforcement learning: synthesizing efficient exploration and effective generalization.

Zheng Wen, Daniel O'Neill, Hamid Reza Maei

Demand response (DR) for residential and small commercial buildings is estimated to account for as much as 65% of the total energy savings potential of DR, and previous work shows that a fully automated Energy Management System (EMS) is a necessary prerequisite to DR in these areas. In this paper, we propose a novel EMS formulation for DR problems in these sectors. Specifically, we formulate a fully automated EMS's rescheduling problem as a reinforcement learning (RL) problem, and argue that this RL problem can be approximately solved by decomposing it over device clusters. Compared with existing formulations, our new formulation (1) does not require explicitly modeling the user's dissatisfaction on job rescheduling, (2) enables the EMS to self-initiate jobs, (3) allows the user to initiate more flexible requests and (4) has a computational complexity linear in the number of devices. We also demonstrate the simulation results of applying Q-learning, one of the most popular and classical RL algorithms, to a representative example.

Zheng Wen, Benjamin Van Roy

We consider the problem of reinforcement learning over episodes of a finite-horizon deterministic system and as a solution propose optimistic constraint propagation (OCP), an algorithm designed to synthesize efficient exploration and value function generalization. We establish that when the true value function lies within a given hypothesis class, OCP selects optimal actions over all but at most K episodes, where K is the eluder dimension of the given hypothesis class. We establish further efficiency and asymptotic performance guarantees that apply even if the true value function does not lie in the given hypothesis class, for the special case where the hypothesis class is the span of pre-specified indicator functions over disjoint sets. We also discuss the computational complexity of OCP and present computational results involving two illustrative examples.