arXiv subjects

Aranyak Mehta

Publications and source records attributed to Aranyak Mehta.

At least 19 recordsLinked to original sources

arXiv2026

The Power of Recruiting the Smaller Side: Two Additional Traders Suffice in Two-Sided Markets

We study Bulow-Klemperer-style competition complexity in two-sided double auctions with $m$ unit-demand buyers drawn i.i.d. from $F_B$ and $n$ unit-supply sellers drawn i.i.d. from $F_S$. When $m \ge n$ and buyer valuations first-order stochastically dominate seller costs ($F_B \succeq_{\mathrm{FSD}} F_S$), we prove that recruiting just two additional sellers enables Seller Trade Reduction (STR), a prior-independent mechanism, to achieve expected Gains From Trade (GFT) at least the first-best GFT of the original market. When the buyer side is the smaller side of the market ($m \le n$), an analogous result holds for Buyer Trade Reduction with 2 additional buyers. This resolves open questions of Babaioff, Goldner, and Gonczarowski (SODA 2020) and Cai, Liaw, Mehta, and Zhao (STOC 2024). We complement our upper bound by showing that this uniform bound is optimal: already for $m = n = 1$, no prior-free mechanism (deterministic or randomized) that is dominant-strategy incentive-compatible, individually rational, and weakly budget-balanced can match the first-best GFT by recruiting only one additional seller.

cs.GT↗

arXiv2026

Improved Revenue Guarantees for Selling Separately and Bundling

We study how much revenue a seller can lose by restricting attention to selling separately or grand bundling, in the setting of a single additive buyer with independent item values. Although revenue-optimal mechanisms can require lotteries and infinite menus, Babaioff, Immorlica, Lucier, and Weinberg showed that the better of these two simple formats always achieves a constant fraction of optimal revenue. We prove that $\mathrm{OPT} \le 3.52 \max\{\mathrm{SREV}, \mathrm{BREV}\}$, where $\mathrm{SREV}$ and $\mathrm{BREV}$ are the optimal revenues from selling separately and grand bundling, respectively. This improves the previous best-known approximation factor of $5.2$ due to Ma and Simchi-Levi and narrows the gap to the known lower bound of $2$.

cs.GT↗

arXiv2026

Prediction with Expert Advice: Anytime Regret with Many Experts Matches the Fixed-Time Constant

Prediction with expert advice is a fundamental problem in online learning. When the time horizon $T$ is known in advance, the minimax cumulative regret over $n$ experts is asymptotically $\sqrt{\frac{T \ln n}{2}}$. This is achieved by the Multiplicative Weights Update algorithm with a learning rate tuned to $T$, and is known to be tight. If instead the regret bound is required to hold simultaneously at every time $t$, the best known guarantee has been $\sqrt{t \ln n}$---a factor of $\sqrt{2}$ worse---and it has remained unknown whether this factor of $\sqrt{2}$ is necessary. We show that it is not. We give an algorithm, requiring no knowledge of the horizon, whose cumulative regret satisfies $R_t \le \bigl(1 + O(\sqrt{\ln \ln n / \ln n})\bigr)\sqrt{t \ln n / 2}$ simultaneously for every $t \ge 1$.

stat.ML↗

arXiv2026

Efficient Online Inverse Optimization with $O(d)$ Regret

We give a deterministic algorithm for online inverse linear optimization with regret $O(d)$, uniform in the horizon and $O(d^{2})$ time per round. A bound of this order was obtained recently by Dewasurendra, settling a question of Gollapudi et al.\ and of Oki and Sakaue, but by an improper rule that enumerates covers at every scale and costs $T^{Θ(d)}$ a round; ours is the first efficient such bound and the first proper one. We build on the variable-metric framework of Sakaue et al., adding a self-normalized rank-one update, and we replace the $\log\det$ potential by the trace power $\tr(H^{-1/2})$, which is bounded outright and removes the $\ln T$. The bound also holds against an expert that does not optimize, and we give corruption-robust and rank-adaptive variants, and an application to convex minimization.

cs.LG↗

arXiv2026

From Compensation Design to Budget-Feasible Mechanisms: A Constant Approximation for Subadditive Valuations

Budget-feasible mechanism design is a classic framework introduced by Singer, but there is still a wide gap between existing upper and lower bounds. In this paper, we significantly advance the state of the art. First, without computational constraints, we show that there exists a universally truthful budget-feasible mechanism with the following approximation ratios: - $3$ for monotone submodular valuations and $e+1$ for nonmonotone submodular valuations, improving over $3.798$ and $9.742$, respectively. - $e+1$ for XOS valuations, improving over $28$. In large markets, our approximation can be improved deterministically to $e$. - $2e+1$ for subadditive valuations, improving over $33$. In large markets, our approximation can be improved deterministically to $2e$. Moreover, for subadditive valuations, we obtain a constant-approximation mechanism that runs in polynomial time using demand queries. This improves over the previous best approximation of $O(\log \log n)$, resolving a long-standing open problem going back to Dobzinski, Papadimitriou, and Singer, who conjectured that a constant approximation requires exponentially many demand queries. We obtain these results through a simple and unifying framework based on non-truthful indirect mechanisms, recently coined compensation design. In particular, through a potential argument, we establish constant price-of-stability bounds for compensation design based on marginal-contribution payment rules, which we then translate into truthful direct mechanisms. For subadditive valuations, the core of the argument is a new smoothing lemma showing that every subadditive function can be approximated within a factor of $2$ by a self-bounding function. This is also of independent interest, readily addressing an open question in multiwinner elections by showing the existence of a $2e$-approximate core even under subadditive valuations.

cs.GT↗

arXiv2026

Compensation Design

We introduce compensation design, the problem of designing payment rules that incentivize high-quality contributions in decentralized environments. Here, a budget-constrained principal with a monotone submodular value function aims to design a payment rule, while agents decide whether to opt in or out depending on their private cost. We show that a simple cost-oblivious and anonymous marginal-contribution payment rule guarantees that pure Nash equilibria always exist and attain a price of anarchy (PoA) of at most $2+o_λ(1)$ in the large-market regime ($λ\to 0$) where each individual cost is at most a $λ$ fraction of the budget. We further show that the factor $2$ is unavoidable among deterministic cost-oblivious rules. Surprisingly, we identify a counterexample showing that a payment rule based on the Shapley value may admit no pure Nash equilibria. We then extend our scope to coarse correlated equilibria. This is further motivated by our intractability result: although a pure Nash equilibrium always exists, computing one is PLS-complete. We establish that coarse correlated equilibria also attain a PoA bound of at most $2+o_λ(1)$, and this guarantee in fact extends even under the payment rule induced by the Shapley value. Moreover, we move beyond monotone submodular value functions and binary actions. First, for (monotone) XOS valuations, we show that no oracle-efficient payment rule can attain a PoA bound of $O(n^{1/2 - ε})$. Second, for submodular but non-monotone valuations, we show that a broad class of natural payment rules fails to guarantee a bounded PoA. Finally, we extend compensation design to the setting where each agent has a combinatorial action set. We provide randomized payment rules with logarithmic PoA guarantees for subadditive values, and matching lower bounds that apply even in the single-agent additive-value setting.

cs.GT↗

arXiv2026

One Model, Two Markets: Bid-Aware Generative Recommendation

Generative Recommender Systems using semantic ids, such as TIGER (Rajput et al., 2023), have emerged as a widely adopted competitive paradigm in sequential recommendation. However, existing architectures are designed solely for semantic retrieval and do not address concerns such as monetization via ad revenue and incorporation of bids for commercial retrieval. We propose GEM-Rec, a unified framework that integrates commercial relevance and monetization objectives directly into the generative sequence. We introduce control tokens to decouple the decision of whether to show an ad from which item to show. This allows the model to learn valid placement patterns directly from interaction logs, which inherently reflect past successful ad placements. Complementing this, we devise a Bid-Aware Decoding mechanism that handles real-time pricing, injecting bids directly into the inference process to steer the generation toward high-value items. We prove that this approach guarantees allocation monotonicity, ensuring that higher bids weakly increase an ad's likelihood of being shown without requiring model retraining. Experiments demonstrate that GEM-Rec allows platforms to dynamically optimize for semantic relevance and platform revenue.

cs.IR↗

arXiv2026

A New Lower Bound for the Random Offerer Mechanism in Bilateral Trade using AI-Guided Evolutionary Search

The celebrated Myerson--Satterthwaite theorem shows that in bilateral trade, no mechanism can be simultaneously fully efficient, Bayesian incentive compatible (BIC), and budget balanced (BB). This naturally raises the question of how closely the gains from trade (GFT) achievable by a BIC and BB mechanism can approximate the first-best (fully efficient) benchmark. The optimal BIC and BB mechanism is typically complex and highly distribution-dependent, making it difficult to characterize directly. Consequently, much of the literature analyzes simpler mechanisms such as the Random-Offerer (RO) mechanism and establishes constant-factor guarantees relative to the first-best GFT. An important open question concerns the worst-case performance of the RO mechanism relative to first-best (FB) efficiency. While it was originally hypothesized that the approximation ratio $\frac{\text{GFT}_{\text{FB}}}{\text{GFT}_{\text{RO}}}$ is bounded by $2$, recent work provided counterexamples to this conjecture: Cai et al. proved that the ratio can be strictly larger than $2$, and Babaioff et al. exhibited an explicit example with ratio approximately $2.02$. In this work, we employ AlphaEvolve, an AI-guided evolutionary search framework, to explore the space of value distributions. We identify a new worst-case instance that yields an improved lower bound of $\frac{\text{GFT}_{\text{FB}}}{\text{GFT}_{\text{RO}}} \ge \textbf{2.0749}$. This establishes a new lower bound on the worst-case performance of the Random-Offerer mechanism, demonstrating a wider efficiency gap than previously known.

cs.LG↗

arXiv2026

Scaling Inference-Time Computation via Opponent Simulation: Enabling Online Strategic Adaptation in Repeated Negotiation

While large language models (LLMs) have emerged as powerful decision-makers across a wide range of single-agent and stationary environments, fewer efforts have been devoted to settings where LLMs must engage in \emph{repeated} and \emph{strategic} interactions with unknown or dynamic opponents. In such settings, recipes built upon \emph{offline} pre-training or fine-tuning, though robust against worst-case adversaries, do not fully exploit the capability of LLMs to adapt \emph{online} based on interaction feedback. Instead, we explore the more natural perspective of scaling inference-time computation as a mechanism for adaptation, embedding the principles of a classical game-theoretical learning dynamic, \emph{smooth Fictitious Play (sFP)}, into LLM inference: (i) for belief formation, we employ an auxiliary opponent model that in-context learns to imitate the time-averaged behavior of the opponent; (ii) for best response, we advance best-of-$N$ (BoN) sampling by simulating against the opponent model. Empirical evaluations on two distinct forms of repeated negotiation games demonstrate that our method enables significant performance improvement over repeated online interaction compared to various baselines, offering a scalable and principled approach to repeated strategic decision-making without any parameter updates.

cs.MA↗

arXiv2026

Incentive-Aligned Multi-Source LLM Summaries

Large language models (LLMs) are increasingly used in modern search and answer systems to synthesize multiple, sometimes conflicting, texts into a single response, yet current pipelines offer weak incentives for sources to be accurate and are vulnerable to adversarial content. We introduce Truthful Text Summarization (TTS), an incentive-aligned framework that improves factual robustness without ground-truth labels. TTS (i) decomposes a draft synthesis into atomic claims, (ii) elicits each source's stance on every claim, (iii) scores sources with an adapted multi-task peer-prediction mechanism that rewards informative agreement, and (iv) filters unreliable sources before re-summarizing. We establish formal guarantees that align a source's incentives with informative honesty, making truthful reporting the utility-maximizing strategy. Experiments show that TTS improves factual accuracy and robustness while preserving fluency, aligning exposure with informative corroboration and disincentivizing manipulation.

cs.CL↗

arXiv2026

Inference-time Unlearning Using Conformal Prediction

Machine unlearning is the process of efficiently removing specific information from a trained machine learning model without retraining from scratch. Existing unlearning methods, which often provide provable guarantees, typically involve retraining a subset of model parameters based on a forget set. While these approaches show promise in certain scenarios, their underlying assumptions are often challenged in real-world applications -- particularly when applied to generative models. Furthermore, updating parameters using these unlearning procedures often degrades the general-purpose capabilities the model acquired during pre-training. Motivated by these shortcomings, this paper considers the paradigm of inference time unlearning -- wherein, the generative model is equipped with an (approximately correct) verifier that judges whether the model's response satisfies appropriate unlearning guarantees. This paper introduces a framework that iteratively refines the quality of the generated responses using feedback from the verifier without updating the model parameters. The proposed framework leverages conformal prediction to reduce computational overhead and provide distribution-free unlearning guarantees. This paper's approach significantly outperforms existing state-of-the-art methods, reducing unlearning error by up to 93% across challenging unlearning benchmarks.

cs.LG↗

arXiv2025

The Average-Value Allocation Problem

We initiate the study of centralized algorithms for welfare-maximizing allocation of goods to buyers subject to average-value constraints. We show that this problem is NP-hard to approximate beyond a factor of $\frac{e}{e-1}$, and provide a $\frac{4e}{e-1}$-approximate offline algorithm. For the online setting, we show that no non-trivial approximations are achievable under adversarial arrivals. Under i.i.d. arrivals, we present a polytime online algorithm that provides a constant approximation of the optimal (computationally-unbounded) online algorithm. In contrast, we show that no constant approximation of the ex-post optimum is achievable by an online algorithm.

cs.DS↗

arXiv2025

Position Auctions in AI-Generated Content

We consider an extension to the classic position auctions in which sponsored creatives can be added within AI generated content rather than shown in predefined slots. New challenges arise from the natural requirement that sponsored creatives should smoothly fit into the context. With the help of advanced LLM technologies, it becomes viable to accurately estimate the benefits of adding each individual sponsored creatives into each potential positions within the AI generated content by properly taking the context into account. Therefore, we assume one click-through rate estimation for each position-creative pair, rather than one uniform estimation for each sponsored creative across all positions in classic settings. As a result, the underlying optimization becomes a general matching problem, thus the substitution effects should be treated more carefully compared to standard position auction settings, where the slots are independent with each other. In this work, we formalize a concrete mathematical model of the extended position auction problem and study the welfare-maximization and revenue-maximization mechanism design problem. Formally, we consider two different user behavior models and solve the mechanism design problems therein respectively. For the Multinomial Logit (MNL) model, which is order-insensitive, we can efficiently implement the optimal mechanisms. For the cascade model, which is order-sensitive, we provide approximately optimal solutions.

cs.GT↗

arXiv2025

Equilibria and Learning in Modular Marketplaces

We envision a marketplace where diverse entities offer specialized "modules" through APIs, allowing users to compose the outputs of these modules for complex tasks within a given budget. This paper studies the market design problem in such an ecosystem, where module owners strategically set prices for their APIs (to maximize their profit) and a central platform orchestrates the aggregation of module outputs at query-time. One can also think about this as a first-price procurement auction with budgets. The first observation is that if the platform's algorithm is to find the optimal set of modules then this could result in a poor outcome, in the sense that there are price equilibria which provide arbitrarily low value for the user. We show that under a suitable version of the "bang-per-buck" algorithm for the knapsack problem, an $\varepsilon$-approximate equilibrium always exists, for any arbitrary $\varepsilon > 0$. Further, our first main result shows that with this algorithm any such equilibrium provides a constant approximation to the optimal value that the buyer could get under various constraints including (i) a budget constraint and (ii) a budget and a matroid constraint. Finally, we demonstrate that these efficient equilibria can be learned through decentralized price adjustments by module owners using no-regret learning algorithms.

cs.GT↗

arXiv2025

Ads in Conversations

We study the optimal placement of advertisements for interactive platforms like conversational AI assistants. Importantly, conversations add a feature absent in canonical search markets -- time. The evolution of a conversation is informative about ad qualities, thus a platform could delay ad delivery to improve selection. However, delay endogenously shapes the supply of quality ads, possibly affecting revenue. We characterize the equilibria of first- and second-price auctions where the platform can commit to the auction format but not to its timing. We document sharp differences in the mechanisms' outcomes: first-price auctions are efficient but delay ad delivery, while second-price auctions avoid delay but allocate inefficiently. Revenue may be arbitrarily larger in a second-price auction than in a first-price auction. Optimal reserve prices alleviate these differences but flip the revenue ordering.

econ.TH↗

arXiv2024

Conditional Language Policy: A General Framework for Steerable Multi-Objective Finetuning

Reward-based finetuning is crucial for aligning language policies with intended behaviors (e.g., creativity and safety). A key challenge is to develop steerable language models that trade-off multiple (conflicting) objectives in a flexible and efficient manner. This paper presents Conditional Language Policy (CLP), a general framework for finetuning language models on multiple objectives. Building on techniques from multi-task training and parameter-efficient finetuning, CLP learn steerable models that effectively trade-off conflicting objectives at inference time. Notably, this does not require training or maintaining multiple models to achieve different trade-offs between the objectives. Through extensive experiments and ablations on two summarization datasets, we show that CLP learns steerable language models that outperform and Pareto-dominate the existing approaches for multi-objective finetuning.

cs.LG↗

arXiv2024

Linear Transformer Topological Masking with Graph Random Features

When training transformers on graph-structured data, incorporating information about the underlying topology is crucial for good performance. Topological masking, a type of relative position encoding, achieves this by upweighting or downweighting attention depending on the relationship between the query and keys in a graph. In this paper, we propose to parameterise topological masks as a learnable function of a weighted adjacency matrix -- a novel, flexible approach which incorporates a strong structural inductive bias. By approximating this mask with graph random features (for which we prove the first known concentration bounds), we show how this can be made fully compatible with linear attention, preserving $\mathcal{O}(N)$ time and space complexity with respect to the number of input tokens. The fastest previous alternative was $\mathcal{O}(N \log N)$ and only suitable for specific graphs. Our efficient masking algorithms provide strong performance gains for tasks on image and point cloud data, including with $>30$k nodes.

cs.LG↗

arXiv2024

Auto-bidding and Auctions in Online Advertising: A Survey

In this survey, we summarize recent developments in research fueled by the growing adoption of automated bidding strategies in online advertising. We explore the challenges and opportunities that have arisen as markets embrace this autobidding and cover a range of topics in this area, including bidding algorithms, equilibrium analysis and efficiency of common auction formats, and optimal auction design.

cs.GT↗