arXiv subjects

Vijay Kamble

Publications and source records attributed to Vijay Kamble.

14 recordsLinked to original sources

arXiv2026

Causal Multi-Task Demand Learning

We study a canonical multi-task demand-learning problem motivated by retail pricing, where a firm seeks to estimate heterogeneous linear price-response functions across multiple decision contexts. Each context is described by rich covariates but exhibits limited price variation, motivating transfer learning across tasks. A central challenge in leveraging cross-task transfer is endogeneity: prices may be arbitrarily correlated with unobserved task-level demand determinants across tasks. We propose a new meta-learning framework that identifies the conditional mean of task-specific causal demand parameters given a subset of task-specific observables despite such confounding, assuming that each task contains at least two distinct locally exogenous price points. This subset is carefully designed to include all of the prices to address cross-task confounding, while masking two demand outcomes that provide randomized supervision to address identifiability issues arising from the inclusion of all prices. We show that this information design is maximally uniformly valid, in that any refinement of the conditioning set that reveals withheld-outcome information is not guaranteed to identify the conditional mean causal target. We validate our method on real and synthetic data, demonstrating improved recovery of demand responses relative to standard transfer-learning baselines.

cs.LG↗

arXiv2024

Price Competition Under A Consider-Then-Choose Model With Lexicographic Choice

The sorting and filtering capabilities offered by modern e-commerce platforms significantly impact customers' purchase decisions, as well as the resulting prices set by competing sellers on these platforms. Motivated by this practical reality, we study price competition under a flexible choice model: Consider-then-Choose with Lexicographic Choice (CLC). In this model, a customer first forms a consideration set of sellers based on (i) her willingness-to-pay and (ii) an arbitrary set of criteria on items' non-price attributes; she then chooses the highest-ranked item according to a lexicographic ranking in which items with better performance on more important attributes are ranked higher. We provide a structural characterization of equilibria in the resulting game of price competition, and derive an economically interpretable condition, which we call gradient dominance, under which equilibria can be computed efficiently. For this subclass of CLC models, we prove that distributed gradient-based pricing dynamics converge to the set of equilibria. Extensive numerical experiments show robustness of our theoretical findings when gradient dominance does not hold.

cs.GT↗

arXiv2022

The Square Root Agreement Rule for Incentivizing Truthful Feedback on Online Platforms

A major challenge in obtaining evaluations of products or services on e-commerce platforms is eliciting informative responses in the absence of verifiability. This paper proposes the Square Root Agreement Rule (SRA): a simple reward mechanism that incentivizes truthful responses to objective evaluations on such platforms. In this mechanism, an agent gets a reward for an evaluation only if her answer matches that of her peer, where this reward is inversely proportional to a popularity index of the answer. This index is defined to be the square root of the empirical frequency at which any two agents performing the same evaluation agree on the particular answer across evaluations of similar entities operating on the platform. Rarely agreed-upon answers thus earn a higher reward than answers for which agreements are relatively more common. We show that in the many tasks regime, the truthful equilibrium under SRA is strictly payoff-dominant across large classes of natural equilibria that could arise in these settings, thus increasing the likelihood of its adoption. While there exist other mechanisms achieving such guarantees, they either impose additional assumptions on the response distribution that are not generally satisfied for objective evaluations or they incentivize truthful behavior only if each agent performs a prohibitively large number of evaluations and commits to using the same strategy for each evaluation. SRA is the first known incentive mechanism satisfying such guarantees without imposing any such requirements. Moreover, our empirical findings demonstrate the robustness of the incentive properties of SRA in the presence of mild subjectivity or observational biases in the responses. These properties make SRA uniquely attractive for administering reward-based incentive schemes (e.g., rebates, discounts, reputation scores, etc.) on online platforms.

cs.GT↗

arXiv2021

Algorithmic Challenges in Ensuring Fairness at the Time of Decision

Algorithmic decision-making in societal contexts, such as retail pricing, loan administration, recommendations on online platforms, etc., can be framed as stochastic optimization under bandit feedback, which typically requires experimentation with different decisions for the sake of learning. Such experimentation often results in perceptions of unfairness among people impacted by these decisions; for instance, there have been several recent lawsuits accusing companies that deploy algorithmic pricing practices of price gouging. Motivated by the changing legal landscape surrounding algorithmic decision-making, we introduce the well-studied fairness notion of envy-freeness within the context of stochastic convex optimization. Our notion requires that upon receiving decisions in the present time, groups do not envy the decisions received by any of the other groups, both in the present as well as the past. This results in a novel trajectory-constrained stochastic optimization problem that renders existing techniques inapplicable. The main technical contribution of this work is to show problem settings where there is no gap in achievable regret (up to logarithmic factors) when envy-freeness is imposed. In particular, in our main result, we develop a near-optimal envy-free algorithm that achieves $\tilde{O}(\sqrt{T})$ regret for smooth convex functions that satisfy the PL inequality. This algorithm has a coordinate-descent structure, in which we carefully leverage gradient information to ensure monotonic sampling along each dimension, while avoiding overshooting the constrained optimum with high probability. This latter aspect critically uses smoothness and the structure of the envy-freeness constraints, while the PL inequality allows for sufficient progress towards the optimal solution. We discuss several open questions that arise from this analysis, which may be of independent interest.

cs.LG↗

arXiv2020

An Approximate Dynamic Programming Approach to Adversarial Online Learning

We describe an approximate dynamic programming (ADP) approach to compute approximations of the optimal strategies and of the minimal losses that can be guaranteed in discounted repeated games with vector-valued losses. Such games prominently arise in the analysis of regret in repeated decision-making in adversarial environments, also known as adversarial online learning. At the core of our approach is a characterization of the lower Pareto frontier of the set of expected losses that a player can guarantee in these games as the unique fixed point of a set-valued dynamic programming operator. When applied to the problem of regret minimization with discounted losses, our approach yields algorithms that achieve markedly improved performance bounds compared to off-the-shelf online learning algorithms like Hedge. These results thus suggest the significant potential of ADP-based approaches in adversarial online learning.

cs.GT↗

arXiv2020

Matching while Learning

We consider the problem faced by a service platform that needs to match limited supply with demand but also to learn the attributes of new users in order to match them better in the future. We introduce a benchmark model with heterogeneous "workers" (demand) and a limited supply of "jobs" that arrive over time. Job types are known to the platform, but worker types are unknown and must be learned by observing match outcomes. Workers depart after performing a certain number of jobs. The expected payoff from a match depends on the pair of types and the goal is to maximize the steady-state rate of accumulation of payoff. Though we use terminology inspired by labor markets, our framework applies more broadly to platforms where a limited supply of heterogeneous products is matched to users over time. Our main contribution is a complete characterization of the structure of the optimal policy in the limit that each worker performs many jobs. The platform faces a trade-off for each worker between myopically maximizing payoffs (exploitation) and learning the type of the worker (exploration). This creates a multitude of multi-armed bandit problems, one for each worker, coupled together by the constraint on availability of jobs of different types (capacity constraints). We find that the platform should estimate a shadow price for each job type, and use the payoffs adjusted by these prices, first, to determine its learning goals and then, for each worker, (i) to balance learning with payoffs during the "exploration phase," and (ii) to myopically match after it has achieved its learning goals during the "exploitation phase."

cs.LG↗

arXiv2020

Maximal Objectives in the Multi-armed Bandit with Applications

In several applications of the stochastic multi-armed bandit problem, the traditional objective of maximizing the expected total reward can be inappropriate. In this paper, motivated by certain operational concerns in online platforms, we consider a new objective in the classical setup. Given $K$ arms, instead of maximizing the expected total reward from $T$ pulls (the traditional "sum" objective), we consider the vector of total rewards earned from each of the $K$ arms at the end of $T$ pulls and aim to maximize the expected highest total reward across arms (the "max" objective). For this objective, we show that any policy must incur an instance-dependent asymptotic regret of $\Omega(\log T)$ (with a higher instance-dependent constant compared to the traditional objective) and a worst-case regret of $\Omega(K^{1/3}T^{2/3})$. We then design an adaptive explore-then-commit policy featuring exploration based on appropriately tuned confidence bounds on the mean reward and an adaptive stopping criterion, which adapts to the problem difficulty and achieves these bounds (up to logarithmic factors). We then generalize our algorithmic insights to the problem of maximizing the expected value of the average total reward of the top $m$ arms with the highest total rewards. Our numerical experiments demonstrate the efficacy of our policies compared to several natural alternatives in practical parameter regimes. We discuss applications of these new objectives to the problem of grooming an adequate supply of value-providing market participants (workers/sellers/service providers) in online platforms.

cs.LG↗

arXiv2019

Revenue Management on an On-Demand Service Platform

I consider the optimal hourly (or per-unit-time in general) pricing problem faced by a freelance worker (or a service provider) on an on-demand service platform. Service requests arriving while the worker is busy are lost forever. Thus, the optimal hourly prices need to capture the average hourly opportunity costs incurred by accepting jobs. Due to potential asymmetries in these costs, price discrimination across jobs based on duration, characteristics of the arrival process, etc., may be necessary for optimality, even if the customers' hourly willingness to pay is identically distributed. I first establish that such price discrimination is not necessary if the customer arrival process is Poisson: in this case, the optimal policy charges an identical hourly rate for all jobs. This result holds even if the earnings are discounted over time. I then consider the case where the customers belong to different classes that are differentiated in their willingness to pay. I present a simple and practical iterative procedure to compute the optimal prices in this case under standard regularity assumptions on the distributions of customer valuations. I finally show that these insights continue to hold in the presence of competition between multiple quality-differentiated workers, assuming a natural customer choice model in which a customer always chooses the best available worker that she can afford.

cs.GT↗

arXiv2019

Individual Fairness in Hindsight

Since many critical decisions impacting human lives are increasingly being made by algorithms, it is important to ensure that the treatment of individuals under such algorithms is demonstrably fair under reasonable notions of fairness. One compelling notion proposed in the literature is that of individual fairness (IF), which advocates that similar individuals should be treated similarly (Dwork et al. 2012). Originally proposed for offline decisions, this notion does not, however, account for temporal considerations relevant for online decision-making. In this paper, we extend the notion of IF to account for the time at which a decision is made, in settings where there exists a notion of conduciveness of decisions as perceived by the affected individuals. We introduce two definitions: (i) fairness-across-time (FT) and (ii) fairness-in-hindsight (FH). FT is the simplest temporal extension of IF where treatment of individuals is required to be individually fair relative to the past as well as future, while in FH, we require a one-sided notion of individual fairness that is defined relative to only the past decisions. We show that these two definitions can have drastically different implications in the setting where the principal needs to learn the utility model. Linear regret relative to optimal individually fair decisions is inevitable under FT for non-trivial examples. On the other hand, we design a new algorithm: Cautious Fair Exploration (CaFE), which satisfies FH and achieves sub-linear regret guarantees for a broad range of settings. We characterize lower bounds showing that these guarantees are order-optimal in the worst case. FH can thus be embedded as a primary safeguard against unfair discrimination in algorithmic deployments, without hindering the ability to take good decisions in the long-run.

cs.LG↗

arXiv2018

Iterative Local Voting for Collective Decision-making in Continuous Spaces

Many societal decision problems lie in high-dimensional continuous spaces not amenable to the voting techniques common for their discrete or single-dimensional counterparts. These problems are typically discretized before running an election or decided upon through negotiation by representatives. We propose a algorithm called {\sc Iterative Local Voting} for collective decision-making in this setting. In this algorithm, voters are sequentially sampled and asked to modify a candidate solution within some local neighborhood of its current value, as defined by a ball in some chosen norm, with the size of the ball shrinking at a specified rate. We first prove the convergence of this algorithm under appropriate choices of neighborhoods to Pareto optimal solutions with desirable fairness properties in certain natural settings: when the voters' utilities can be expressed in terms of some form of distance from their ideal solution, and when these utilities are additively decomposable across dimensions. In many of these cases, we obtain convergence to the societal welfare maximizing solution. We then describe an experiment in which we test our algorithm for the decision of the U.S. Federal Budget on Mechanical Turk with over 2,000 workers, employing neighborhoods defined by $\mathcal{L}^1, \mathcal{L}^2$ and $\mathcal{L}^\infty$ balls. We make several observations that inform future implementations of such a procedure.

cs.MA↗

arXiv2018

Exploration vs. Exploitation in Team Formation

An online labor platform faces an online learning problem in matching workers with jobs and using the performance on these jobs to create better future matches. This learning problem is complicated by the rise of complex tasks on these platforms, such as web development and product design, that require a team of workers to complete. The success of a job is now a function of the skills and contributions of all workers involved, which may be unknown to both the platform and the client who posted the job. These team matchings result in a structured correlation between what is known about the individuals and this information can be utilized to create better future matches. We analyze two natural settings where the performance of a team is dictated by its strongest and its weakest member, respectively. We find that both problems pose an exploration-exploitation tradeoff between learning the performance of untested teams and repeating previously tested teams that resulted in a good performance. We establish fundamental regret bounds and design near-optimal algorithms that uncover several insights into these tradeoffs.

cs.LG↗

arXiv2015

Approximately Optimal Scheduling of an M/G/1 Queue with Heavy Tails

Distributions with a heavy tail are difficult to estimate. If the design of a scheduling policy is sensitive to the details of heavy tail distributions of the service times, an approximately optimal solution is difficult to obtain. This paper shows that the optimal scheduling of an M/G/1 queue with heavy tailed service times does not present this difficulty and that an approximately optimal strategy can be derived by truncating the distributions.

math.PR↗

arXiv2015

Monotonic Preference Aggregation Mechanisms for Purchasing a Shareable Resource

Situations where a group of agents come together to jointly buy a resource that they individually cannot afford to buy are commonly observed in markets. For example in the US market for radio spectrum, a recent proposal invited small firms who would benefit from gaining additional access to spectrum to jointly submit bids for blocks of spectrum with the idea that its utilization could be shared. In such a scenario, the problem is to design a mechanism that truthfully elicits and aggregates the privately held preferences of these agents, and enables them to act as a single decision-making body in order to participate in the market. In this paper, we design a class of mechanisms called monotonic aggregation mechanisms that achieves this under a specific setting. We assume that the resource is being sold in a sealed-bid second-price auction that solicits bids for the entire resource. Our mechanism truthfully elicits utility functions from the buyers, prescribes a joint bid, and prescribes a division of the payment and the resource in the event that they win the resource in the auction. This mechanism further satisfies a popular notion of collusion-resistance known as coalition-strategyproofness. We give two explicit examples of this generic class for the case where the utility functions of the buyers are non-decreasing and concave.

cs.GT↗

arXiv2015

Sequential Relevance Maximization with Binary Feedback

Motivated by online settings where users can provide explicit feedback about the relevance of products that are sequentially presented to them, we look at the recommendation process as a problem of dynamically optimizing this relevance feedback. Such an algorithm optimizes the fine tradeoff between presenting the products that are most likely to be relevant, and learning the preferences of the user so that more relevant recommendations can be made in the future. We assume a standard predictive model inspired by collaborative filtering, in which a user is sampled from a distribution over a set of possible types. For every product category, each type has an associated relevance feedback that is assumed to be binary: the category is either relevant or irrelevant. Assuming that the user stays for each additional recommendation opportunity with probability $β$ independent of the past, the problem is to find a policy that maximizes the expected number of recommendations that are deemed relevant in a session. We analyze this problem and prove key structural properties of the optimal policy. Based on these properties, we first present an algorithm that strikes a balance between recursion and dynamic programming to compute this policy. We further propose and analyze two heuristic policies: a `farsighted' greedy policy that attains at least $1-β$ factor of the optimal payoff, and a naive greedy policy that attains at least $\frac{1-β}{1+β}$ factor of the optimal payoff in the worst case. Extensive simulations show that these heuristics are very close to optimal in practice.

cs.LG↗