We introduce and study the online Bayesian recommendation problem for a recommender system platform. The platform has the privilege to privately observe a utilityrelevant state of a product at each round and uses this information to make online recommendations to a stream of myopic users. This paradigm is common in a wide range of scenarios in the current internet economy. The platform commits to an online recommendation policy that utilizes its information advantage on the product state to persuade self-interested users to follow the recommendation. Because the platform does not know users' preferences or beliefs in advance, we study the platform's online learning problem of designing an adaptive recommendation policy to persuade users while gradually learning users' preferences and beliefs en route. Specifically, we aim to design online learning policies with no Stackelberg regret for the platform, that is, against the optimal benchmark policy in hindsight under the assumption that users will correspondingly adapt their responses to the benchmark policy. Our first result is an online policy that achieves double logarithmic regret dependence on the number of rounds. We also present an information-theoretic lower bound showing that no adaptive online policy can achieve regret with better dependency on the number of rounds. Finally, by formulating the platform's problem as optimizing a linear program with membership oracle access, we present our second online recommendation policy that achieves regret with polynomial dependence on the number of states but logarithmic dependence on the number of rounds.

The integration of AI Overviews into search engines enhances user experience but diverts traffic from content creators, potentially discouraging high-quality content creation and causing user attrition that undermines long-term search engine profit. To address this issue, we propose a game-theoretic model of creator competition with costly effort, characterize equilibrium behavior, and design two incentive mechanisms: a citation mechanism that references sources within an AI Overview, and a compensation mechanism that offers monetary rewards to creators. For both cases, we provide structural insights and near-optimal profit-maximizing mechanisms. Evaluations on real click data show that although AI Overviews harm long-term search engine profit, interventions based on our proposed mechanisms can increase long-term profit across a range of realistic scenarios, pointing toward a more sustainable trajectory for AI-enhanced search ecosystems.

Coordinating agents through hazardous environments, such as aid-delivering drones navigating conflict zones or field robots traversing deployment areas filled with obstacles, poses fundamental planning challenges. We introduce and analyze the computational complexity of a new multi-agent path planning problem that captures this setting. A group of identical agents begins at a common start location and must navigate a graph-based environment to reach a common target. The graph contains hazards that eliminate agents upon contact but then enter a known cooldown period before reactivating. In this discrete-time, fully-observable, deterministic setting, the planning task is to compute a movement schedule that maximizes the number of agents reaching the target. We first prove that, despite the exponentially large space of feasible plans, optimal plans require only polynomially-many steps, establishing membership in NP. We then show that the problem is NP-hard even when the environment graph is a tree. On the positive side, we present a polynomial-time algorithm for graphs consisting of vertex-disjoint paths from start to target. Our results establish a rich computational landscape for this problem, identifying both intractable and tractable fragments.

With the rapid advancement of generative AI (GenAI), mechanism design adapted to its unique characteristics poses new theoretical and practical challenges. Unlike traditional goods, content from one domain can enhance the training and performance of GenAI models in other domains. For example, OpenAI's video generation model Sora (Liu et al., 2024b) relies heavily on image data to improve video generation quality. In this work, we study nonlinear procurement mechanism design under data transferability, where online platforms employ both human creators and GenAI to satisfy cross-domain content demand. We propose optimal mechanisms that maximize either platform revenue or social welfare and identify the specific properties of GenAI that make such high-dimensional design problems tractable. Our analysis further reveals which domains face stronger competitive pressure and which tend to experience overproduction. Moreover, the growing role of data intermediaries, including labeling companies such as Scale AI and creator organizations such as The Wall Street Journal, introduces a third layer into the traditional platform-creator structure. We show that this three-layer market can result in a lose-lose outcome, reducing both platform revenue and social welfare, as large pre-signed contracts distort creators' incentives and lead to inefficiencies in the data market. These findings suggest a need for government regulation of the GenAI data ecosystem, and our theoretical insights are further supported by numerical simulations.

Prediction markets aggregate dispersed beliefs into prices that act as probabilistic forecasts of uncertain events. Classical theory establishes a clean equivalence between forecasting accuracy and trading profit, but only for the specific automated market maker (AMM) design. However, the largest exchanges today are based on central limit order books in which informed forecasters routinely lose money while uninformed strategies can profit on simple heuristics. We resolve this discrepancy by establishing a formal equivalence between predictive accuracy and profitability. For any strictly proper scoring rule S, we exhibit a "proper" betting strategy that depends only on the forecaster's prediction 𝐩 and the market price 𝐪, and earns positive expected profit whenever 𝐩 outperforms 𝐪 under S and the market has sufficient liquidity. Moreover, this proper betting is essentially the only strategy with such robust profitability guarantee. The proof rests on a decomposition of expected profit that strictly generalizes the classical AMM guarantee and also explains how strategies can profit without an accuracy edge. Empirically, across thousands of forecasts by AI models, proper betting is the only strategy that reliably converts accuracy into profit, and we further identify systematic forecasting personas and show how the optimal proper strategy varies across them. A month-long live deployment on Kalshi achieves +80.33% return on investment with a Sharpe ratio of 3.35.

Performance manipulation arises when agents exploit easily measurable, routine tasks to inflate observable outcomes without contributing genuine innovation or expert judgment. We formalize this phenomenon in a game-theoretic model in which agents allocate effort along two margins. Creative effort is non-routine cognitive labor whose return is complementary to the agent's private expertise; it is the scarce input that principals seek. Mechanistic effort is the execution of well-defined, rule-based tasks that raise performance independently of expertise, a commoditized input that AI heavily augments. We establish the existence of a symmetric, monotone pure-strategy equilibrium and show that performance-based screening remains viable so long as evaluations retain a sufficient creative component, but collapses into an uninformative pooling equilibrium once AI capability grows large enough to crowd out creative effort. Comparing contest allocations against a single-agent baseline isolates performance manipulation as the competition-induced over-investment in mechanistic effort, which we show is undertaken systematically by low-type agents but not high-type ones. We further prove that more sharply skewed reward structures mitigate this friction by eliciting greater creative effort across the participant pool. Finally, using a novel, language-model-based methodology to measure both effort types from nearly 1,500 Kaggle competition scripts, we provide robust empirical support for the model's predictions.

The probabilistic bisection algorithm (PBA) extends the classical binary search to settings with noisy responses, and is a foundational algorithm commonly used in basic problems such as root-finding. Despite its strong empirical success, its theoretical property, particularly the convergence rate, remains unclear. This paper establishes that PBA converges at a geometric rate, providing a rigorous justification for its empirical efficiency. Notably, this rate is optimal in the sense that it matches the performance of classical binary search under noiseless responses. The core of our analysis lies in directly characterizing the dynamics of PBA queries, which had not been examined in the prior literature. We show that the queries oscillate around the truth but steadily draw closer, thus leading to an estimator that rapidly concentrates on the truth. Beyond resolving the long-standing question of PBA’s convergence, our developed techniques offer new tools for analyzing PBA's dynamics, which may be of independent interest.

We study a variant of the principal-agent problem in which the principal does not directly observe the outcomes; rather, she gets a signal related to the agent's action, according to a variable information structure. We provide simple necessary and sufficient conditions for implementability of an action and a utility profile by some information structure and the corresponding optimal contract - for a risk-neutral or risk-averse agent, with or without the limited liability assumption. It turns out that the set of implementable utility profiles is characterized by simple thresholds on the utilities.

Synthetic data has been increasingly used to train frontier generative models. However, recent study raises key concerns that iteratively retraining a generative model on its self-generated synthetic data may keep deteriorating model performance, a phenomenon often coined model collapse. In this paper, we investigate ways to modify the synthetic retraining process to avoid model collapse, and even possibly help reverse the trend from collapse to improvement. Our key finding is that by injecting information through an external synthetic data verifier, whether a human or a better model, synthetic retraining will not cause model collapse. Specifically, we situate our theoretical analysis in the fundamental linear regression problem, showing that verifier-guided retraining yields early improvements when the verifier is accurate, and in the long run, the parameter estimate converges to the verifier’s knowledge center. Our theory predicts that the performance of synthetic retraining will have early gains but eventually plateaus or even reverses, unless the verifier is perfectly reliable. Indeed, our experiments on both linear regression as well as Conditional Variational Autoencoder (CVAE) trained on MNIST data also confirm these theoretical insights.

As machine learning models continue to grow in size and complexity, efficient serving faces increasingly broad trade-offs spanning accuracy, latency, resource usage, and other objectives. Multi-model serving further complicates these trade-offs; for example, in cascaded models, each early-exit decision balances latency reduction against potential accuracy loss. Despite the pervasiveness and importance of such trade-offs, current strategies remain largely heuristic and case-specific, limiting both their theoretical guarantees and general applicability. We present a general framework, T-Tamer, which formalizes this setting as a multi-stage decision process, where the objective is to determine both when to exit and which model to consult. Our main result shows that recall (i.e., the ability to revisit earlier models) is both necessary and sufficient for achieving provable performance guarantees. In particular, we prove that strategies without recall cannot obtain any constant-factor approximation to the optimal trade-off, whereas recall-based strategies provably attain the optimal trade-off in polynomial time. We validate our analysis through experiments on synthetic datasets and early-exit workloads for vision and NLP benchmarks. The results show that recall-based strategies consistently yield efficient accuracy–latency trade-offs. We hope this work provides a principled foundation for bridging heuristic practice with theoretical guarantees in the design of early-exit and cascaded models.

With the rapid progress of multi-agent large language model (LLM) reasoning, how to effectively aggregate answers from multiple LLMs has emerged as a fundamental challenge. Standard majority voting treats all answers equally, failing to consider latent heterogeneity and correlation across models. In this work, we design two new aggregation algorithms called Optimal Weight (OW) and Inverse Surprising Popularity (ISP), leveraging both first-order and second-order information. Our theoretical analysis shows these methods provably mitigate the inherent limitations of majority voting under mild assumptions, leading to more reliable collective decisions. We empirically validate our algorithms on synthetic datasets, popular LLM fine-tuning benchmarks such as UltraFeedback and MMLU, and a real-world healthcare setting ARMMAN. Our algorithms consistently outperform standard baselines, establishing a robust, training-free framework for effective multi-agent LLM aggregation.

With the rapid progress of large language models (LLMs) trained on every available piece of data, it becomes increasingly challenging to reliably evaluate their intelligence due to potential data contamination and benchmark overfitting. To overcome these challenges, we investigate a new angle of benchmarking LLMs' intelligence by evaluating their capability in forecasting real-world future events, a paradigm we call "LLM-as-a-Prophet". Such forecasting tasks require combination of sophisticated capabilities while remaining free from data contamination or overfitting. To systematically evaluate such predictive intelligence of LLMs, we introduce $\texttt{Prophet Arena}$, a general evaluation benchmark that continuously collects live forecasting tasks and decomposes each task into distinct pipeline stages, supporting our controlled and large-scale experimentation. Our comprehensive evaluation reveals that many LLMs already exhibit impressive forecasting capabilities, reflected in, e.g., their small calibration errors, consistent prediction confidence and promising market returns. However, we also uncover key bottlenecks even in frontier models, such as inaccurate event recalls, misunderstanding of data sources and slower information aggregation compared to markets when resolution nears.

No-Regret Bayesian Recommendation to Homogeneous Users We introduce and study the online Bayesian recommendation problem for a recommender system platform. The platform has the privilege to privately observe a utility-relevant state of a product at each round and uses this information to make online recommendations to a stream of myopic users. This paradigm is common in a wide range of scenarios in the current internet economy. The platform commits to an online recommendation policy that utilizes its information advantage on the product state to persuade self-interested users to follow the recommendation. Because the platform does not know users’ preferences or beliefs in advance, we study the platform’s online learning problem of designing an adaptive recommendation policy to persuade users while gradually learning users’ preferences and beliefs en route. Specifically, we aim to design online learning policies with no Stackelberg regret for the platform, that is, against the optimal benchmark policy in hindsight under the assumption that users will correspondingly adapt their responses to the benchmark policy. Our first result is an online policy that achieves double logarithmic regret dependence on the number of rounds. We also present an information-theoretic lower bound showing that no adaptive online policy can achieve regret with better dependency on the number of rounds. Finally, by formulating the platform’s problem as optimizing a linear program with membership oracle access, we present our second online recommendation policy that achieves regret with polynomial dependence on the number of states but logarithmic dependence on the number of rounds.

Generative AI (GenAI) will have significant impact on content creation platforms. In this paper, we study the dynamic competition between a GenAI and a human contributor. Unlike the human, the GenAI's content only improves when more contents are created by the human over time; however, GenAI has the advantage of generating content at a lower cost. We study the algorithmic problem in this dynamic competition model about how the human contributor can maximize her utility when competing against the GenAI for content generation over a set of topics. In time-sensitive content domains (e.g., news or pop music creation) where contents' value diminishes over time, we show that there is no polynomial time algorithm for finding the human's optimal (dynamic) strategy, unless the randomized exponential time hypothesis is false. Fortunately, we are able to design a polynomial time algorithm that naturally cycles between myopically optimizing over a short time window and pausing and provably guarantees an approximation ratio of 1/2. We then turn to time-insensitive content domains where contents do not lose their value (e.g., contents on history facts). Interestingly, we show that this setting permits a polynomial time algorithm that maximizes the human's utility in the long run. Finally, we conduct simulations that demonstrate the advantage of our algorithms in comparison to a collection of baselines.

Data markets promise to unlock data value by matching data suppliers with ML consumers. However, market design involves addressing intricate challenges, including data pricing, fairness, and robustness. We propose a pragmatic data-augmented AutoML market that seamlessly integrates with existing cloud-based AutoML platforms, such as Google’s Vertex AI. Unlike standard AutoML solutions, our design automatically augments buyer-submitted training data with valuable external datasets, pricing the resulting models based on their measurable performance improvements rather than computational costs as the status quo. Our key innovation is a pricing mechanism grounded in the instrumental value—the marginal model quality improvement—of externally sourced data. This approach bypasses direct dataset pricing complexities and accommodates diverse buyer valuations through menu-based options, thus providing an economically sustainable framework for monetizing external data.

Researchers strategically choose where to submit their work in order to maximize its impact, and these publication decisions in turn determine venues' impact factors. To analyze how individual publication choices both respond to and shape venue impact, we introduce a game-theoretic framework - coined the Publication Choice Problem - that captures this two‐way interplay. We show the existence of a pure-strategy equilibrium in the Publication Choice Problem and its uniqueness under binary researcher types. Our characterizations of the equilibrium properties offer insights about what publication behaviors better indicate a researcher's impact level. Through equilibrium analysis, we further investigate how labeling papers with ``spotlight'' affects the impact factor of venues in the research community. Our analysis shows that competitive venue labeling top papers with ``spotlight'' may decrease the overall impact of other venues in the community, while less competitive venues with ``spotlight'' labeling have an opposite impact.

Fine-tuning is often believed to reduce uncertainty and diversity in large language models, but existing analyses overlook output length, a key confounder, and therefore fail to capture how uncertainty is distributed across an entire generation rollout. To address this, we propose Canopy Entropy (CE^⋆), a measure that views language generation from a tree perspective, where “canopy” represents the space of all possible rollouts, making CE^⋆ naturally quantify the effective size of the generation space. CE^⋆ jointly captures uncertainty in both the output length N and the generated sequence Y_1:N – indeed, we show that it equals to total Shannon entropy H(N, Y_1:N| X), where X denotes the prompt. This formulation yields interpretable metrics, including a length-entropy correlation term ρ(N, r_N), where r_N is the entropy rate, quantifying information conveyance efficiency by indicating whether longer outputs are more or less informative per token. Empirically, across tasks and model families, we find that fine-tuned models consistently exhibit stronger positive correlation ρ(N, r_N), even when total entropy decreases. Furthermore, after controlling for model family, task, prompt, and output-length effects, we find that fine-tuning nearly triples the correlation strength between entropy rate and semantic diversity, suggesting that aligned models convert token uncertainty into semantic diversity more efficiently. Overall, these results demonstrate that fine-tuning does not simply reduce uncertainty, but fundamentally reorganizes it into more informative and semantically meaningful generations. Our code is available at https://github.com/WeiyiTian/canopy-entropy.

In this paper, we study the Markovian Pandora's Box Problem, where decisions are governed by both order constraints and Markovianly correlated rewards, structured within a shared directed acyclic graph. To the best of our knowledge, previous work has not incorporated Markovian dependencies in this setting. This framework is particularly relevant to applications such as data or computation driven algorithm design, where exploration of future models incurs cost. We present optimal fully adaptive strategies where the associated graph forms a forest. Under static transition, we introduce a strategy that achieves a near optimal expected payoff in multi line graphs and a 1/2 approximation in forest-structured graphs. Notably, this algorithm provides a significant speedup over the exact solution, with the improvement becoming more pronounced as the graph size increases. Our findings deepen the understanding of sequential exploration under Markovian correlations in graph-based decision-making.

Decades of research in machine learning have given us powerful tools for making accurate predictions. But when used in social settings and on human inputs, better accuracy does not immediately translate to better social outcomes. To effectively promote social well-being through machine learning, this position article advocates for the wide adoption of social welfare as a guiding principle. The field of welfare economics asks: how should we allocate limited resources to self-interested agents in a way that maximizes social benefit? We argue that this perspective applies to many modern applications of machine learning in social contexts. As such, we propose that welfare serves as an additional core criterion in the design, study, and use of learning algorithms, complementing the conventional pillars of optimization, generalization, and expressivity, and as a compass guiding both theory and practice.