We propose TETRIS, a novel method that optimizes the total throughput of batch speculative decoding in multi-request settings. Unlike existing methods that optimize for a single request or a group of requests as a whole, TETRIS actively selects the most promising draft tokens (for every request in a batch) to be accepted when verified in parallel, resulting in fewer rejected tokens and hence less wasted computing resources. Such an effective resource utilization to achieve fast inference in large language models (LLMs) is especially important to service providers with limited inference capacity. Compared to baseline speculative decoding, TETRIS yields a consistently higher acceptance rate and more effective utilization of the limited inference capacity. We show theoretically and empirically that TETRIS outperforms baseline speculative decoding and existing methods that dynamically select draft tokens, leading to a more efficient batch inference in LLMs.

Large language models (LLMs) have demonstrated remarkable performances in various tasks. However, the performance of LLMs heavily depends on the input prompt, which has given rise to a number of recent works on prompt optimization. However, previous works often require the availability of a numeric score to assess the quality of every prompt. Unfortunately, when a human user interacts with a black-box LLM, attaining such a score is often infeasible and unreliable. Instead, it is usually significantly easier and more reliable to obtain preference feedback from a human user, i.e., showing the user the responses generated from a pair of prompts and asking the user which one is preferred. Therefore, in this paper, we study the problem of prompt optimization with human feedback (POHF), in which we aim to optimize the prompt for a black-box LLM using only human preference feedback. Drawing inspiration from dueling bandits, we design a theoretically principled strategy to select a pair of prompts to query for preference feedback in every iteration, and hence introduce our algorithm named automated POHF (APOHF). We apply our APOHF algorithm to various tasks, including optimizing user instructions, prompt optimization for text-to-image generative models, and response optimization with human feedback (i.e., further refining the response using a variant of our APOHF). The results demonstrate that our APOHF can efficiently find a good prompt using a small number of preference feedback instances. Our code can be found at \url{https://github.com/xqlin98/APOHF}.

We study a novel variant of the parameterized bandits problem in which the learner can observe additional auxiliary feedback that is correlated with the observed reward. The auxiliary feedback is readily available in many real-life applications, e.g., an online platform that wants to recommend the best-rated services to its users can observe the user's rating of service (rewards) and collect additional information like service delivery time (auxiliary feedback). In this paper, we first develop a method that exploits auxiliary feedback to build a reward estimator with tight confidence bounds, leading to a smaller regret. We then characterize the regret reduction in terms of the correlation coefficient between reward and its auxiliary feedback. Experimental results in different settings also verify the performance gain achieved by our proposed method.

Recent works on neural contextual bandits have achieved compelling performances due to their ability to leverage the strong representation power of neural networks (NNs) for reward prediction. Many applications of contextual bandits involve multiple agents who collaborate without sharing raw observations, thus giving rise to the setting of federated contextual bandits. Existing works on federated contextual bandits rely on linear or kernelized bandits, which may fall short when modeling complex real-world reward functions. So, this paper introduces the federated neural-upper confidence bound (FN-UCB) algorithm. To better exploit the federated setting, FN-UCB adopts a weighted combination of two UCBs: $\text{UCB}^{a}$ allows every agent to additionally use the observations from the other agents to accelerate exploration (without sharing raw observations), while $\text{UCB}^{b}$ uses an NN with aggregated parameters for reward prediction in a similar way to federated averaging for supervised learning. Notably, the weight between the two UCBs required by our theoretical analysis is amenable to an interesting interpretation, which emphasizes $\text{UCB}^{a}$ initially for accelerated exploration and relies more on $\text{UCB}^{b}$ later after enough observations have been collected to train the NNs for accurate reward prediction (i.e., reliable exploitation). We prove sub-linear upper bounds on both the cumulative regret and the number of communication rounds of FN-UCB, and empirically demonstrate its competitive performance.

This thesis considers sequential decision problems, where the loss/reward incurred by selecting an action may not be inferred from observed feedback. A major part of this thesis focuses on the unsupervised sequential selection problem, where one can not infer the loss incurred for selecting an action from observed feedback. We also introduce a new setup named Censored Semi Bandits, where the loss incurred for selecting an action can be observed under certain conditions. Finally, we study the channel selection problem in the communication networks, where the reward for an action is only observed when no other player selects that action to play in the round. These problems find applications in many fields like healthcare, crowd-sourcing, security, adaptive resource allocation, among many others. This thesis aims to address the above-described sequential decision problems by exploiting specific structures these problems exhibit. We develop provably optimal algorithms for each of these setups with weak feedback and validate their empirical performance on different problem instances derived from synthetic and real datasets.

This paper studies a new variant of the stochastic multi-armed bandits problem, where the learner has access to auxiliary information about the arms. The auxiliary information is correlated with the arm rewards, which we treat as control variates. In many applications, the arm rewards are a function of some exogenous values, whose mean value is known a priori from historical data and hence can be used as control variates. We use the control variates to obtain mean estimates with smaller variance and tighter confidence bounds. We then develop an algorithm named UCB-CV that uses improved estimates. We characterize the regret bounds in terms of the correlation between the rewards and control variates. The experiments on synthetic data validate the performance guarantees of our proposed algorithm.

We consider the problem of sequentially allocating resources in a censored semi-bandits setup, where the learner allocates resources at each step to the arms and observes loss. The loss depends on two hidden parameters, one specific to the arm but independent of the resource allocation, and the other depends on the allocated resource. More specifically, the loss equals zero for an arm if the resource allocated to it exceeds a constant (but unknown) arm dependent threshold. The goal is to learn a resource allocation that minimizes the expected loss. The problem is challenging because the loss distribution and threshold value of each arm are unknown. We study this setting by establishing its `equivalence' to Multiple-Play Multi-Armed Bandits (MP-MAB) and Combinatorial Semi-Bandits. Exploiting these equivalences, we derive optimal algorithms for our problem setting using known algorithms for MP-MAB and Combinatorial Semi-Bandits. The experiments on synthetically generated data validate the performance guarantees of the proposed algorithms.

In this paper, we study Contextual Unsupervised Sequential Selection (USS), a new variant of the stochastic contextual bandits problem where the loss of an arm cannot be inferred from the observed feedback. In our setup, arms are associated with fixed costs and are ordered, forming a cascade. In each round, a context is presented, and the learner selects the arms sequentially till some depth. The total cost incurred by stopping at an arm is the sum of fixed costs of arms selected and the stochastic loss associated with the arm. The learner's goal is to learn a decision rule that maps contexts to arms with the goal of minimizing the total expected loss. The problem is challenging as we are faced with an unsupervised setting as the total loss cannot be estimated. Clearly, learning is feasible only if the optimal arm can be inferred (explicitly or implicitly) from the problem structure. We observe that learning is still possible when the problem instance satisfies the so-called 'Contextual Weak Dominance' (CWD) property. Under CWD, we propose an algorithm for the contextual USS problem and demonstrate that it has sub-linear regret. Experiments on synthetic and real datasets validate our algorithm.

Thompson Sampling has generated significant interest due to its better empirical performance than upper confidence bound based algorithms. In this paper, we study Thompson Sampling based algorithm for Unsupervised Sequential Selection (USS) problem. The USS problem is a variant of the stochastic multi-armed bandits problem, where the loss of an arm can not be inferred from the observed feedback. In the USS setup, arms are associated with fixed costs and are ordered, forming a cascade. In each round, the learner selects an arm and observes the feedback from arms up to the selected arm. The learner's goal is to find the arm that minimizes the expected total loss. The total loss is the sum of the cost incurred for selecting the arm and the stochastic loss associated with the selected arm. The problem is challenging because, without knowing the mean loss, one cannot compute the total loss for the selected arm. Clearly, learning is feasible only if the optimal arm can be inferred from the problem structure. As shown in the prior work, learning is possible when the problem instance satisfies the so-called `Weak Dominance' (WD) property. Under WD, we show that our Thompson Sampling based algorithm for the USS problem achieves near optimal regret and has better numerical performance than existing algorithms.

In this paper, we study a novel Stochastic Network Utility Maximization (NUM) problem where the utilities of agents are unknown. The utility of each agent depends on the amount of resource it receives from a network operator/controller. The operator desires to do a resource allocation that maximizes the expected total utility of the network. We consider threshold type utility functions where each agent gets non-zero utility if the amount of resource it receives is higher than a certain threshold. Otherwise, its utility is zero (hard real-time). We pose this NUM setup with unknown utilities as a regret minimization problem. Our goal is to identify a policy that performs as `good' as an oracle policy that knows the utilities of agents. We model this problem setting as a bandit setting where feedback obtained in each round depends on the resource allocated to the agents. We propose algorithms for this novel setting using ideas from Multiple-Play Multi-Armed Bandits and Combinatorial Semi-Bandits. We show that the proposed algorithm is optimal when all agents have the same utility. We validate the performance guarantees of our proposed algorithms through numerical experiments.