Soumya Basu

Soumya Basu, Ankit Singh Rawat, Manzil Zaheer

Many modern high-performing machine learning models such as GPT-3 primarily rely on scaling up models, e.g., transformer networks. Simultaneously, a parallel line of work aims to improve the model performance by augmenting an input instance with other (labeled) instances during inference. Examples of such augmentations include task-specific prompts and similar examples retrieved from the training data by a nonparametric component. Remarkably, retrieval-based methods have enjoyed success on a wide range of problems, ranging from standard natural language processing and vision tasks to protein folding, as demonstrated by many recent efforts, including WebGPT and AlphaFold. Despite growing literature showcasing the promise of these models, the theoretical underpinning for such models remains underexplored. In this paper, we present a formal treatment of retrieval-based models to characterize their generalization ability. In particular, we focus on two classes of retrieval-based classification approaches: First, we analyze a local learning framework that employs an explicit local empirical risk minimization based on retrieved examples for each input instance. Interestingly, we show that breaking down the underlying learning task into local sub-tasks enables the model to employ a low complexity parametric component to ensure good overall accuracy. The second class of retrieval-based approaches we explore learns a global model using kernel methods to directly map an input instance and retrieved examples to a prediction, without explicitly solving a local learning task.

Soumya Basu, Ankit Singh Rawat, Manzil Zaheer

Modern ML systems increasingly augment input instances with additional relevant information to enhance final prediction. Despite growing interest in such retrieval-augmented models, their fundamental properties and training are not well understood. We propose a statistical framework to study such models with two components: 1) a {\em retriever} to identify the relevant information out of a large corpus via a data-dependent metric; and 2) a {\em predictor} that consumes the input instances along with the retrieved information to make the final predictions. We present a principled method for end-to-end training of both components and draw connections with various training approaches in the literature. Furthermore, we establish excess risk bounds for retrieval-augmented models while delineating the contributions of both retriever and predictor towards the model performance. We validate the utility of our proposed training methods along with the key takeaways from our statistical analysis on open domain question answering task where retrieval augmentation is important.

Soumya Basu, Abishek Sankararaman

Double Auction enables decentralized transfer of goods between multiple buyers and sellers, thus underpinning functioning of many online marketplaces. Buyers and sellers compete in these markets through bidding, but do not often know their own valuation a-priori. As the allocation and pricing happens through bids, the profitability of participants, hence sustainability of such markets, depends crucially on learning respective valuations through repeated interactions. We initiate the study of Double Auction markets under bandit feedback on both buyers' and sellers' side. We show with confidence bound based bidding, and `Average Pricing' there is an efficient price discovery among the participants. In particular, the regret on combined valuation of the buyers and the sellers -- a.k.a. the social regret -- is $O(\log(T)/Δ)$ in $T$ rounds, where $Δ$ is the minimum price gap. Moreover, the buyers and sellers exchanging goods attain $O(\sqrt{T})$ regret, individually. The buyers and sellers who do not benefit from exchange in turn only experience $O(\log{T}/ Δ)$ regret individually in $T$ rounds. We augment our upper bound by showing that $ω(\sqrt{T})$ individual regret, and $ω(\log{T})$ social regret is unattainable in certain Double Auction markets. Our paper is the first to provide decentralized learning algorithms in a two-sided market where \emph{both sides have uncertain preference} that need to be learned.

Soumya Basu

We study bandit learning in matching markets with two-sided reward uncertainty, extending prior research primarily focused on single-sided uncertainty. Leveraging the concept of `super-stability' from Irving (1994), we demonstrate the advantage of the Extended Gale-Shapley (GS) algorithm over the standard GS algorithm in achieving true stable matchings under incomplete information. By employing the Extended GS algorithm, our centralized algorithm attains a logarithmic pessimal stable regret dependent on an instance-dependent admissible gap parameter. This algorithm is further adapted to a decentralized setting with a constant regret increase. Finally, we establish a novel centralized instance-dependent lower bound for binary stable regret, elucidating the roles of the admissible gap and super-stable matching in characterizing the complexity of stable matching with bandit feedback.

Satush Parikh, Soumya Basu, Avishek Ghosh et al.

Sequential learning in a multi-agent resource constrained matching market has received significant interest in the past few years. We study decentralized learning in two-sided matching markets where the demand side (aka players or agents) competes for the supply side (aka arms) with potentially time-varying preferences to obtain a stable match. Motivated by the linear contextual bandit framework, we assume that for each agent, an arm-mean may be represented by a linear function of a known feature vector and an unknown (agent-specific) parameter. Moreover, the preferences over arms depend on a latent environment in each round, where the latent environment varies across rounds in a non-stationary manner. We propose learning algorithms to identify the latent environment and obtain stable matchings simultaneously. Our proposed algorithms achieve instance-dependent logarithmic regret, scaling independently of the number of arms, and hence applicable for a large market.

Soumya Basu, Branislav Kveton, Manzil Zaheer et al.

We propose ${\tt AdaTS}$, a Thompson sampling algorithm that adapts sequentially to bandit tasks that it interacts with. The key idea in ${\tt AdaTS}$ is to adapt to an unknown task prior distribution by maintaining a distribution over its parameters. When solving a bandit task, that uncertainty is marginalized out and properly accounted for. ${\tt AdaTS}$ is a fully-Bayesian algorithm that can be implemented efficiently in several classes of bandit problems. We derive upper bounds on its Bayes regret that quantify the loss due to not knowing the task prior, and show that it is small. Our theory is supported by experiments, where ${\tt AdaTS}$ outperforms prior algorithms and works well even in challenging real-world problems.

Nihal Sharma, Rajat Sen, Soumya Basu et al.

We study a variant of the contextual bandit problem where an agent can intervene through a set of stochastic expert policies. Given a fixed context, each expert samples actions from a fixed conditional distribution. The agent seeks to remain competitive with the 'best' among the given set of experts. We propose the Divergence-based Upper Confidence Bound (D-UCB) algorithm that uses importance sampling to share information across experts and provide horizon-independent constant regret bounds that only scale linearly in the number of experts. We also provide the Empirical D-UCB (ED-UCB) algorithm that can function with only approximate knowledge of expert distributions. Further, we investigate the episodic setting where the agent interacts with an environment that changes over episodes. Each episode can have different context and reward distributions resulting in the best expert changing across episodes. We show that by bootstrapping from $\mathcal{O}\left(N\log\left(NT^2\sqrt{E}\right)\right)$ samples, ED-UCB guarantees a regret that scales as $\mathcal{O}\left(E(N+1) + \frac{N\sqrt{E}}{T^2}\right)$ for $N$ experts over $E$ episodes, each of length $T$. We finally empirically validate our findings through simulations.

Alexia Atsidakou, Orestis Papadigenopoulos, Soumya Basu et al.

Recent work has considered natural variations of the multi-armed bandit problem, where the reward distribution of each arm is a special function of the time passed since its last pulling. In this direction, a simple (yet widely applicable) model is that of blocking bandits, where an arm becomes unavailable for a deterministic number of rounds after each play. In this work, we extend the above model in two directions: (i) We consider the general combinatorial setting where more than one arms can be played at each round, subject to feasibility constraints. (ii) We allow the blocking time of each arm to be stochastic. We first study the computational/unconditional hardness of the above setting and identify the necessary conditions for the problem to become tractable (even in an approximate sense). Based on these conditions, we provide a tight analysis of the approximation guarantee of a natural greedy heuristic that always plays the maximum expected reward feasible subset among the available (non-blocked) arms. When the arms' expected rewards are unknown, we adapt the above heuristic into a bandit algorithm, based on UCB, for which we provide sublinear (approximate) regret guarantees, matching the theoretical lower bounds in the limiting case of absence of delays.

Soumya Basu, Karthik Abinav Sankararaman, Abishek Sankararaman

We design decentralized algorithms for regret minimization in the two-sided matching market with one-sided bandit feedback that significantly improves upon the prior works (Liu et al. 2020a, 2020b, Sankararaman et al. 2020). First, for general markets, for any $\varepsilon > 0$, we design an algorithm that achieves a $O(\log^{1+\varepsilon}(T))$ regret to the agent-optimal stable matching, with unknown time horizon $T$, improving upon the $O(\log^{2}(T))$ regret achieved in (Liu et al. 2020b). Second, we provide the optimal $Θ(\log(T))$ agent-optimal regret for markets satisfying uniqueness consistency -- markets where leaving participants don't alter the original stable matching. Previously, $Θ(\log(T))$ regret was achievable (Sankararaman et al. 2020, Liu et al. 2020b) in the much restricted serial dictatorship setting, when all arms have the same preference over the agents. We propose a phase-based algorithm, wherein each phase, besides deleting the globally communicated dominated arms the agents locally delete arms with which they collide often. This local deletion is pivotal in breaking deadlocks arising from rank heterogeneity of agents across arms. We further demonstrate the superiority of our algorithm over existing works through simulations.

Ashish Katiyar, Soumya Basu, Vatsal Shah et al.

We study the problem of learning tree-structured Markov random fields (MRF) on discrete random variables with common support when the observations are corrupted by a $k$-ary symmetric noise channel with unknown probability of error. For Ising models (support size = 2), past work has shown that graph structure can only be recovered up to the leaf clusters (a leaf node, its parent, and its siblings form a leaf cluster) and exact recovery is impossible. No prior work has addressed the setting of support size of 3 or more, and indeed this setting is far richer. As we show, when the support size is 3 or more, the structure of the leaf clusters may be partially or fully identifiable. We provide a precise characterization of this phenomenon and show that the extent of recoverability is dictated by the joint PMF of the random variables. In particular, we provide necessary and sufficient conditions for exact recoverability. Furthermore, we present a polynomial time, sample efficient algorithm that recovers the exact tree when this is possible, or up to the unidentifiability as promised by our characterization, when full recoverability is impossible. Finally, we demonstrate the efficacy of our algorithm experimentally.

Vatsal Shah, Soumya Basu, Anastasios Kyrillidis et al.

Over-parameterization and adaptive methods have played a crucial role in the success of deep learning in the last decade. The widespread use of over-parameterization has forced us to rethink generalization by bringing forth new phenomena, such as implicit regularization of optimization algorithms and double descent with training progression. A series of recent works have started to shed light on these areas in the quest to understand -- why do neural networks generalize well? The setting of over-parameterized linear regression has provided key insights into understanding this mysterious behavior of neural networks. In this paper, we aim to characterize the performance of adaptive methods in the over-parameterized linear regression setting. First, we focus on two sub-classes of adaptive methods depending on their generalization performance. For the first class of adaptive methods, the parameter vector remains in the span of the data and converges to the minimum norm solution like gradient descent (GD). On the other hand, for the second class of adaptive methods, the gradient rotation caused by the pre-conditioner matrix results in an in-span component of the parameter vector that converges to the minimum norm solution and the out-of-span component that saturates. Our experiments on over-parameterized linear regression and deep neural networks support this theory.

Advait Parulekar, Soumya Basu, Aditya Gopalan et al.

We study a variant of the stochastic linear bandit problem wherein we optimize a linear objective function but rewards are accrued only orthogonal to an unknown subspace (which we interpret as a \textit{protected space}) given only zero-order stochastic oracle access to both the objective itself and protected subspace. In particular, at each round, the learner must choose whether to query the objective or the protected subspace alongside choosing an action. Our algorithm, derived from the OFUL principle, uses some of the queries to get an estimate of the protected space, and (in almost all rounds) plays optimistically with respect to a confidence set for this space. We provide a $\tilde{O}(sd\sqrt{T})$ regret upper bound in the case where the action space is the complete unit ball in $\mathbb{R}^d$, $s < d$ is the dimension of the protected subspace, and $T$ is the time horizon. Moreover, we demonstrate that a discrete action space can lead to linear regret with an optimistic algorithm, reinforcing the sub-optimality of optimism in certain settings. We also show that protection constraints imply that for certain settings, no consistent algorithm can have a regret smaller than $Ω(T^{3/4}).$ We finally empirically validate our results with synthetic and real datasets.

Abishek Sankararaman, Soumya Basu, Karthik Abinav Sankararaman

Online learning in a two-sided matching market, with demand side agents continuously competing to be matched with supply side (arms), abstracts the complex interactions under partial information on matching platforms (e.g. UpWork, TaskRabbit). We study the decentralized serial dictatorship setting, a two-sided matching market where the demand side agents have unknown and heterogeneous valuation over the supply side (arms), while the arms have known uniform preference over the demand side (agents). We design the first decentralized algorithm -- UCB with Decentralized Dominant-arm Deletion (UCB-D3), for the agents, that does not require any knowledge of reward gaps or time horizon. UCB-D3 works in phases, where in each phase, agents delete \emph{dominated arms} -- the arms preferred by higher ranked agents, and play only from the non-dominated arms according to the UCB. At the end of the phase, agents broadcast in a decentralized fashion, their estimated preferred arms through {\em pure exploitation}. We prove both, a new regret lower bound for the decentralized serial dictatorship model, and that UCB-D3 is order optimal.

Soumya Basu, Orestis Papadigenopoulos, Constantine Caramanis et al.

We study a novel variant of the multi-armed bandit problem, where at each time step, the player observes an independently sampled context that determines the arms' mean rewards. However, playing an arm blocks it (across all contexts) for a fixed and known number of future time steps. The above contextual setting, which captures important scenarios such as recommendation systems or ad placement with diverse users, invalidates greedy solution techniques that are effective for its non-contextual counterpart (Basu et al., NeurIPS19). Assuming knowledge of the context distribution and the mean reward of each arm-context pair, we cast the problem as an online bipartite matching problem, where the right-vertices (contexts) arrive stochastically and the left-vertices (arms) are blocked for a finite number of rounds each time they are matched. This problem has been recently studied in the full-information case, where competitive ratio bounds have been derived. We focus on the bandit setting, where the reward distributions are initially unknown; we propose a UCB-based variant of the full-information algorithm that guarantees a $\mathcal{O}(\log T)$-regret w.r.t. an $α$-optimal strategy in $T$ time steps, matching the $Ω(\log(T))$ regret lower bound in this setting. Due to the time correlations caused by blocking, existing techniques for upper bounding regret fail. For proving our regret bounds, we introduce the novel concepts of delayed exploitation and opportunistic subsampling and combine them with ideas from combinatorial bandits and non-stationary Markov chains coupling.

Nihal Sharma, Soumya Basu, Karthikeyan Shanmugam et al.

We study a variant of the bandit problem where side information in the form of bounds on the mean of each arm is provided. We prove that these translate to tighter estimates of subgaussian factors and develop novel algorithms that exploit these estimates. In the linear setting, we present the Restricted-set OFUL (R-OFUL) algorithm that additionally uses the geometric properties of the problem to (potentially) restrict the set of arms being played and reduce exploration rates for suboptimal arms. In the stochastic case, we propose the non-optimistic Global Under-Explore (GLUE) algorithm which employs the inferred subgaussian estimates to adapt the rate of exploration for the arms. We analyze the regret of R-OFUL and GLUE, showing that our regret upper bounds are never worse than that of the standard OFUL and UCB algorithms respectively. Further, we also consider a practically motivated setting of learning from confounded logs where mean bounds appear naturally.

Soumya Basu, Rajat Sen, Sujay Sanghavi et al.

We consider a novel stochastic multi-armed bandit setting, where playing an arm makes it unavailable for a fixed number of time slots thereafter. This models situations where reusing an arm too often is undesirable (e.g. making the same product recommendation repeatedly) or infeasible (e.g. compute job scheduling on machines). We show that with prior knowledge of the rewards and delays of all the arms, the problem of optimizing cumulative reward does not admit any pseudo-polynomial time algorithm (in the number of arms) unless randomized exponential time hypothesis is false, by mapping to the PINWHEEL scheduling problem. Subsequently, we show that a simple greedy algorithm that plays the available arm with the highest reward is asymptotically $(1-1/e)$ optimal. When the rewards are unknown, we design a UCB based algorithm which is shown to have $c \log T + o(\log T)$ cumulative regret against the greedy algorithm, leveraging the free exploration of arms due to the unavailability. Finally, when all the delays are equal the problem reduces to Combinatorial Semi-bandits providing us with a lower bound of $c' \log T+ ω(\log T)$.

Jessica Hoffmann, Soumya Basu, Surbhi Goel et al.

We consider the problem of learning the weighted edges of a balanced mixture of two undirected graphs from epidemic cascades. While mixture models are popular modeling tools, algorithmic development with rigorous guarantees has lagged. Graph mixtures are apparently no exception: until now, very little is known about whether this problem is solvable. To the best of our knowledge, we establish the first necessary and sufficient conditions for this problem to be solvable in polynomial time on edge-separated graphs. When the conditions are met, i.e., when the graphs are connected with at least three edges, we give an efficient algorithm for learning the weights of both graphs with optimal sample complexity (up to log factors). We give complimentary results and provide sample-optimal (up to log factors) algorithms for mixtures of directed graphs of out-degree at least three, for mixture of undirected graphs of unbalanced and/or unknown priors.

Soumya Basu, David Easley, Maureen O'Hara et al.

Blockchain-based cryptocurrencies prioritize transactions based on their fees, creating a unique kind of fee market. Empirically, this market has failed to yield stable equilibria with predictable prices for desired levels of service. We argue that this is due to the absence of a dominant strategy equilibrium in the current fee mechanism. We propose an alternative fee setting mechanism that is inspired by generalized second price auctions. The design of such a mechanism is challenging because miners can use any criteria for including transactions and can manipulate the results of the auction after seeing the proposed fees. Nonetheless, we show that our proposed protocol is free from manipulation as the number of users increases. We further show that, for a large number of users and miners, the gain from manipulation is small for all parties. This results in users proposing fees that represent their true utility and lower variance of revenue for miners. Historical analysis shows that Bitcoin users could have saved $272,528,000 USD in transaction fees while miners could have reduced the variance of fee income by an average factor of 7.4 times.

Soumya Basu, Alin Tomescu, Ittai Abraham et al.

This paper introduces a new way to incorporate verifiable secret sharing (VSS) schemes into Byzantine Fault Tolerance (BFT) protocols. This technique extends the threshold guarantee of classical Byzantine Fault Tolerant algorithms to include privacy as well. This provides applications with a powerful primitive: a threshold trusted third party, which simplifies many difficult problems such as a fair exchange. In order to incorporate VSS into BFT, we introduced sAVSS, a framework that transforms any VSS scheme into an asynchronous VSS scheme with constant overhead. By incorporating Kate et al.'s scheme into our framework, we obtain an asynchronous VSS that has constant overhead on each replica -- the first of its kind. We show that a key-value store built using BFT replication and sAVSS supports writing secret-shared values with about a 30% - 50% throughput overhead with less than 35 millisecond request latencies.

Adem Efe Gencer, Soumya Basu, Ittay Eyal et al.

Blockchain-based cryptocurrencies have demonstrated how to securely implement traditionally centralized systems, such as currencies, in a decentralized fashion. However, there have been few measurement studies on the level of decentralization they achieve in practice. We present a measurement study on various decentralization metrics of two of the leading cryptocurrencies with the largest market capitalization and user base, Bitcoin and Ethereum. We investigate the extent of decentralization by measuring the network resources of nodes and the interconnection among them, the protocol requirements affecting the operation of nodes, and the robustness of the two systems against attacks. In particular, we adapted existing internet measurement techniques and used the Falcon Relay Network as a novel measurement tool to obtain our data. We discovered that neither Bitcoin nor Ethereum has strictly better properties than the other. We also provide concrete suggestions for improving both systems.

Aman Agarwal, Soumya Basu, Tobias Schnabel et al.

Accurately evaluating new policies (e.g. ad-placement models, ranking functions, recommendation functions) is one of the key prerequisites for improving interactive systems. While the conventional approach to evaluation relies on online A/B tests, recent work has shown that counterfactual estimators can provide an inexpensive and fast alternative, since they can be applied offline using log data that was collected from a different policy fielded in the past. In this paper, we address the question of how to estimate the performance of a new target policy when we have log data from multiple historic policies. This question is of great relevance in practice, since policies get updated frequently in most online systems. We show that naively combining data from multiple logging policies can be highly suboptimal. In particular, we find that the standard Inverse Propensity Score (IPS) estimator suffers especially when logging and target policies diverge -- to a point where throwing away data improves the variance of the estimator. We therefore propose two alternative estimators which we characterize theoretically and compare experimentally. We find that the new estimators can provide substantially improved estimation accuracy.