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Abstract:We study the Linear Contextual Bandit problem in the hybrid reward setting. In this setting every arm's reward model contains arm specific parameters in addition to parameters shared across the reward models of all the arms. We can reduce this setting to two closely related settings (a) Shared - no arm specific parameters, and (b) Disjoint - only arm specific parameters, enabling the application of two popular state of the art algorithms - $\texttt{LinUCB}$ and $\texttt{DisLinUCB}$ (Algorithm 1 in (Li et al. 2010)). When the arm features are stochastic and satisfy a popular diversity condition, we provide new regret analyses for both algorithms, significantly improving on the known regret guarantees of these algorithms. Our novel analysis critically exploits the hybrid reward structure and the diversity condition. Moreover, we introduce a new algorithm $\texttt{HyLinUCB}$ that crucially modifies $\texttt{LinUCB}$ (using a new exploration coefficient) to account for sparsity in the hybrid setting. Under the same diversity assumptions, we prove that $\texttt{HyLinUCB}$ also incurs only $O(\sqrt{T})$ regret for $T$ rounds. We perform extensive experiments on synthetic and real-world datasets demonstrating strong empirical performance of $\texttt{HyLinUCB}$.For number of arm specific parameters much larger than the number of shared parameters, we observe that $\texttt{DisLinUCB}$ incurs the lowest regret. In this case, regret of $\texttt{HyLinUCB}$ is the second best and extremely competitive to $\texttt{DisLinUCB}$. In all other situations, including our real-world dataset, $\texttt{HyLinUCB}$ has significantly lower regret than $\texttt{LinUCB}$, $\texttt{DisLinUCB}$ and other SOTA baselines we considered. We also empirically observe that the regret of $\texttt{HyLinUCB}$ grows much slower with the number of arms compared to baselines, making it suitable even for very large action spaces.

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Authors:Ravisri Valluri, Akash Kumar Mohankumar, Kushal Dave, Amit Singh, Jian Jiao, Manik Varma, Gaurav Sinha

Abstract:Generative Retrieval introduces a new approach to Information Retrieval by reframing it as a constrained generation task, leveraging recent advancements in Autoregressive (AR) language models. However, AR-based Generative Retrieval methods suffer from high inference latency and cost compared to traditional dense retrieval techniques, limiting their practical applicability. This paper investigates fully Non-autoregressive (NAR) language models as a more efficient alternative for generative retrieval. While standard NAR models alleviate latency and cost concerns, they exhibit a significant drop in retrieval performance (compared to AR models) due to their inability to capture dependencies between target tokens. To address this, we question the conventional choice of limiting the target token space to solely words or sub-words. We propose PIXAR, a novel approach that expands the target vocabulary of NAR models to include multi-word entities and common phrases (up to 5 million tokens), thereby reducing token dependencies. PIXAR employs inference optimization strategies to maintain low inference latency despite the significantly larger vocabulary. Our results demonstrate that PIXAR achieves a relative improvement of 31.0% in MRR@10 on MS MARCO and 23.2% in Hits@5 on Natural Questions compared to standard NAR models with similar latency and cost. Furthermore, online A/B experiments on a large commercial search engine show that PIXAR increases ad clicks by 5.08% and revenue by 4.02%.

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Abstract:We study a variant of causal contextual bandits where the context is chosen based on an initial intervention chosen by the learner. At the beginning of each round, the learner selects an initial action, depending on which a stochastic context is revealed by the environment. Following this, the learner then selects a final action and receives a reward. Given $T$ rounds of interactions with the environment, the objective of the learner is to learn a policy (of selecting the initial and the final action) with maximum expected reward. In this paper we study the specific situation where every action corresponds to intervening on a node in some known causal graph. We extend prior work from the deterministic context setting to obtain simple regret minimization guarantees. This is achieved through an instance-dependent causal parameter, $\lambda$, which characterizes our upper bound. Furthermore, we prove that our simple regret is essentially tight for a large class of instances. A key feature of our work is that we use convex optimization to address the bandit exploration problem. We also conduct experiments to validate our theoretical results, and release our code at our project GitHub repository: https://github.com/adaptiveContextualCausalBandits/aCCB.

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Abstract:We study the generalized linear contextual bandit problem within the requirements of limited adaptivity. In this paper, we present two algorithms, B-GLinCB and RS-GLinCB, that address, respectively, two prevalent limited adaptivity models: batch learning with stochastic contexts and rare policy switches with adversarial contexts. For both these models, we establish essentially tight regret bounds. Notably, in the obtained bounds, we manage to eliminate a dependence on a key parameter $\kappa$, which captures the non-linearity of the underlying reward model. For our batch learning algorithm B-GLinCB, with $\Omega\left( \log{\log T} \right)$ batches, the regret scales as $\tilde{O}(\sqrt{T})$. Further, we establish that our rarely switching algorithm RS-GLinCB updates its policy at most $\tilde{O}(\log^2 T)$ times and achieves a regret of $\tilde{O}(\sqrt{T})$. Our approach for removing the dependence on $\kappa$ for generalized linear contextual bandits might be of independent interest.

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Authors:Daman Arora, Anush Kini, Sayak Ray Chowdhury, Nagarajan Natarajan, Gaurav Sinha, Amit Sharma

Abstract:Given a query and a document corpus, the information retrieval (IR) task is to output a ranked list of relevant documents. Combining large language models (LLMs) with embedding-based retrieval models, recent work shows promising results on the zero-shot retrieval problem, i.e., no access to labeled data from the target domain. Two such popular paradigms are generation-augmented retrieval or GAR (generate additional context for the query and then retrieve), and retrieval-augmented generation or RAG (retrieve relevant documents as context and then generate answers). The success of these paradigms hinges on (i) high-recall retrieval models, which are difficult to obtain in the zero-shot setting, and (ii) high-precision (re-)ranking models which typically need a good initialization. In this work, we propose a novel GAR-meets-RAG recurrence formulation that overcomes the challenges of existing paradigms. Our method iteratively improves retrieval (via GAR) and rewrite (via RAG) stages in the zero-shot setting. A key design principle is that the rewrite-retrieval stages improve the recall of the system and a final re-ranking stage improves the precision. We conduct extensive experiments on zero-shot passage retrieval benchmarks, BEIR and TREC-DL. Our method establishes a new state-of-the-art in the BEIR benchmark, outperforming previous best results in Recall@100 and nDCG@10 metrics on 6 out of 8 datasets, with up to 17% relative gains over the previous best.

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Abstract:We study the causal bandit problem that entails identifying a near-optimal intervention from a specified set $A$ of (possibly non-atomic) interventions over a given causal graph. Here, an optimal intervention in ${A}$ is one that maximizes the expected value for a designated reward variable in the graph, and we use the standard notion of simple regret to quantify near optimality. Considering Bernoulli random variables and for causal graphs on $N$ vertices with constant in-degree, prior work has achieved a worst case guarantee of $\widetilde{O} (N/\sqrt{T})$ for simple regret. The current work utilizes the idea of covering interventions (which are not necessarily contained within ${A}$) and establishes a simple regret guarantee of $\widetilde{O}(\sqrt{N/T})$. Notably, and in contrast to prior work, our simple regret bound depends only on explicit parameters of the problem instance. We also go beyond prior work and achieve a simple regret guarantee for causal graphs with unobserved variables. Further, we perform experiments to show improvements over baselines in this setting.

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Abstract:In many real-world scenarios, such as gene knockout experiments, targeted interventions are often accompanied by unknown interventions at off-target sites. Moreover, different units can get randomly exposed to different unknown interventions, thereby creating a mixture of interventions. Identifying different components of this mixture can be very valuable in some applications. Motivated by such situations, in this work, we study the problem of identifying all components present in a mixture of interventions on a given causal Bayesian Network. We construct an example to show that, in general, the components are not identifiable from the mixture distribution. Next, assuming that the given network satisfies a positivity condition, we show that, if the set of mixture components satisfy a mild exclusion assumption, then they can be uniquely identified. Our proof gives an efficient algorithm to recover these targets from the exponentially large search space of possible targets. In the more realistic scenario, where distributions are given via finitely many samples, we conduct a simulation study to analyze the performance of an algorithm derived from our identifiability proof.

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Abstract:A well-studied challenge that arises in the structure learning problem of causal directed acyclic graphs (DAG) is that using observational data, one can only learn the graph up to a "Markov equivalence class" (MEC). The remaining undirected edges have to be oriented using interventions, which can be very expensive to perform in applications. Thus, the problem of minimizing the number of interventions needed to fully orient the MEC has received a lot of recent attention, and is also the focus of this work. We prove two main results. The first is a new universal lower bound on the number of atomic interventions that any algorithm (whether active or passive) would need to perform in order to orient a given MEC. Our second result shows that this bound is, in fact, within a factor of two of the size of the smallest set of atomic interventions that can orient the MEC. Our lower bound is provably better than previously known lower bounds. The proof of our lower bound is based on the new notion of clique-block shared-parents (CBSP) orderings, which are topological orderings of DAGs without v-structures and satisfy certain special properties. Further, using simulations on synthetic graphs and by giving examples of special graph families, we show that our bound is often significantly better.

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Abstract:We study Markov Decision Processes (MDP) wherein states correspond to causal graphs that stochastically generate rewards. In this setup, the learner's goal is to identify atomic interventions that lead to high rewards by intervening on variables at each state. Generalizing the recent causal-bandit framework, the current work develops (simple) regret minimization guarantees for two-stage causal MDPs, with parallel causal graph at each state. We propose an algorithm that achieves an instance dependent regret bound. A key feature of our algorithm is that it utilizes convex optimization to address the exploration problem. We identify classes of instances wherein our regret guarantee is essentially tight, and experimentally validate our theoretical results.

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Abstract:We study the problem of determining the best intervention in a Causal Bayesian Network (CBN) specified only by its causal graph. We model this as a stochastic multi-armed bandit (MAB) problem with side-information, where the interventions correspond to the arms of the bandit instance. First, we propose a simple regret minimization algorithm that takes as input a semi-Markovian causal graph with atomic interventions and possibly unobservable variables, and achieves $\tilde{O}(\sqrt{M/T})$ expected simple regret, where $M$ is dependent on the input CBN and could be very small compared to the number of arms. We also show that this is almost optimal for CBNs described by causal graphs having an $n$-ary tree structure. Our simple regret minimization results, both upper and lower bound, subsume previous results in the literature, which assumed additional structural restrictions on the input causal graph. In particular, our results indicate that the simple regret guarantee of our proposed algorithm can only be improved by considering more nuanced structural restrictions on the causal graph. Next, we propose a cumulative regret minimization algorithm that takes as input a general causal graph with all observable nodes and atomic interventions and performs better than the optimal MAB algorithm that does not take causal side-information into account. We also experimentally compare both our algorithms with the best known algorithms in the literature. To the best of our knowledge, this work gives the first simple and cumulative regret minimization algorithms for CBNs with general causal graphs under atomic interventions and having unobserved confounders.

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