arXiv subjects

Hu Fu

Publications and source records attributed to Hu Fu.

At least 19 recordsLinked to original sources

arXiv2026

Emotional Preferences as Goal-Priority Regulation

A core question in decision-making for agents is whether the relative priorities of competing lower-level objectives can be determined by emotional preferences autonomously generated by higher-level goals, rather than being externally prespecified. Under changing external environments and evolving internal states, emotions play an important functional role in regulating the relative priorities of competing goals. Inspired by the goal-directed theory of emotion, this paper studies how such preference regulation can be computationally realized through reinforcement learning. We first propose a conception of emergent emotional preference: a high-level goal autonomously induces state-dependent preferences over competing lower-level objectives. This conception is built upon a framework consisting of a multi-objective reinforcement learning inner controller and an outer preference generator. The inner controller provides a repertoire of preference-conditioned goal-directed behaviors, while the outer preference generator learns a mapping from the current state to objective preferences through reinforcement learning on a high-level goal. We operationalize emotional preference as a state-dependent regulation of relative goal priorities that emerges through optimization. Furthermore, we characterize the policy space induced by preference regulation and derive an upper bound on the optimality gap in terms of the representation error of the inner behavioral repertoire. We show that the gap vanishes when the optimal policy can be represented by the available preference-conditioned policies. Experiments in self-constructed multi-objective exploration environments show that the learned preference function exhibits contextual priority switching, graded trade-offs, and temporal persistence, and outperforms the evaluated fixed-preference and handcrafted-preference strategies.

cs.LG↗

arXiv2026

Algorithmic Information Design for Searchers with Uncertain Alternatives

Advertisements reveal information to consumers who decide on further information acquisition and eventual purchase. Anderson and Renault (2006) first modeled this problem using an information-design framework where the advertiser acts as a sender and the consumer as a receiver. Due to search frictions and the consumer's outside option, search for additional information is not always worthwhile for the receiver. Thus, the sender's information design is used to make further search attractive and ultimately induce purchase. Following Lyu (2023), we study the optimal information design for a sender who sells search goods to a consumer with uncertain alternatives. Instead of making relaxations to the sender's problem (as done in Lyu, 2023), we work directly on the joint distribution over realized values and signals. Our contributions are twofold. First, we give a method, based on duality arguments, to verify whether a given information strategy is optimal. We illustrate the value of this verification framework in a competitive extension, where it certifies a non-trivial symmetric equilibrium for two senders with a common convex prior. Second, on the algorithmic front, we develop an FPTAS that finds for the seller a signaling scheme whose utility differs from that of the optimal solution by at most an additive $\epsilon$ error, for any $\epsilon > 0$.

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arXiv2025

Learning to Coordinate Bidders in Non-Truthful Auctions

In non-truthful auctions such as first-price and all-pay auctions, the independent strategic behaviors of bidders, with the corresponding Bayes-Nash equilibrium notion, are notoriously difficult to characterize and can cause undesirable outcomes. An alternative approach to achieve better outcomes in non-truthful auctions is to coordinate the bidders: let a mediator make incentive-compatible recommendations of correlated bidding strategies to the bidders, namely, implementing a Bayes correlated equilibrium (BCE). The implementation of BCE, however, requires knowledge of the distributions of bidders' private valuations, which is often unavailable. We initiate the study of the sample complexity of learning Bayes correlated equilibria in non-truthful auctions. We prove that the set of strategic-form BCEs in a large class of non-truthful auctions, including first-price and all-pay auctions, can be learned with a polynomial number $\tilde O(\frac{n}{\varepsilon^2})$ of samples of bidders' values. This moderate number of samples demonstrates the statistical feasibility of learning to coordinate bidders. Our technique is a reduction to the problem of estimating bidders' expected utility from samples, combined with an analysis of the pseudo-dimension of the class of all monotone bidding strategies.

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arXiv2025

Price Stability and Improved Buyer Utility with Presentation Design: A Theoretical Study of the Amazon Buy Box

Platforms design the form of presentation by which sellers are shown to the buyers. This design not only shapes the buyers' experience but also leads to different market equilibria or dynamics. One component in this design is through the platform's mediation of the search frictions experienced by the buyers for different sellers. We take a model of monopolistic competition and show that, on one hand, when all sellers have the same inspection costs, the market sees no stable price since the sellers always have incentives to undercut each other, and, on the other hand, the platform may stabilize the price by giving prominence to one seller chosen by a carefully designed mechanism. This calls to mind Amazon's Buy Box. We study natural mechanisms for choosing the prominent seller, characterize the range of equilibrium prices implementable by them, and find that in certain scenarios the buyers' surplus improves as the search friction increases.

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arXiv2024

Incentives for Early Arrival in Cost Sharing

In cooperative games, we study how values created or costs incurred by a coalition are shared among the members within it, and the players may join the coalition in a online manner such as investors invest a startup. Recently, Ge et al. [10] proposed a new property called incentives for early arrival (I4EA) in such games, which says that the online allocation of values or costs should incentivize agents to join early in order to prevent mutual strategic waiting. Ideally, the allocation should also be fair, so that agents arriving in an order uniformly at random should expect to get/pay their Shapley values. Ge et al. [10] showed that not all monotone value functions admit such mechanisms in online value sharing games. In this work, we show a sharp contrast in online cost sharing games. We construct a mechanism with all the properties mentioned above, for every monotone cost function. To achieve this, we first solve 0-1 valued cost sharing games with a novel mechanism called Shapley-fair shuffle cost sharing mechanism (SFS-CS), and then extend SFS-CS to a family called generalized Shapley-fair shuffle cost sharing mechanisms (GSFS-CS). The critical technique we invented here is a mapping from one arrival order to another order so that we can directly apply marginal cost allocation on the shuffled orders to satisfy the properties. Finally, we solve general valued cost functions, by decomposing them into 0-1 valued functions in an online fashion.

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arXiv2024

Sample-Based Matroid Prophet Inequalities

We study matroid prophet inequalities when distributions are unknown and accessible only through samples. While single-sample prophet inequalities for special matroids are known, no constant-factor competitive algorithm with even a sublinear number of samples was known for general matroids. Adding more to the stake, the single-sample version of the question for general matroids has close (two-way) connections with the long-standing matroid secretary conjecture. In this work, we give a $(\frac14 - \varepsilon)$-competitive matroid prophet inequality with only $O_\varepsilon(\mathrm{poly} \log n)$ samples. Our algorithm consists of two parts: (i) a novel quantile-based reduction from matroid prophet inequalities to online contention resolution schemes (OCRSs) with $O_\varepsilon(\log n)$ samples, and (ii) a $(\frac14 - \varepsilon)$-selectable matroid OCRS with $O_\varepsilon(\mathrm{poly} \log n)$ samples which carefully addresses an adaptivity challenge.

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arXiv2023

Pay to (Not) Play: Monetizing Impatience in Mobile Games

Mobile gaming is a rapidly growing and incredibly profitable sector; having grown seven-fold over the past 10 years, it now grosses over $100 billion annually. This growth was due in large part to a shift in monetization strategies: rather than charging players an upfront cost ("pay-to-play"), games often request optional microtransactions throughout gameplay ("free-to-play"). We focus on a common scenario in which games include wait times -- gating either items or game progression -- that players can pay to skip. Game designers typically say that they optimize for player happiness rather than revenue; however, prices for skips are typically set at levels that few players are willing to pay, leading to low purchase rates. Under a traditional analysis, it would seem that game designers fail at their stated goal if few players buy what they are selling. We argue that an alternate model can better explain this dynamic: players value tasks more highly as they are perceived to be more difficult. While skips can increase players' utilities by providing instant gratification, pricing skips too cheaply can lower players' utilities by decreasing the perceived amount of work needed to complete a task. We show that high revenue, high player utility, and low purchase rates can all coexist under this model, particularly under a realistic distribution of players having few buyers but a few big-spending "whales." We also investigate how a game designer should optimize prices under our model.

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arXiv2023

On the Last-iterate Convergence in Time-varying Zero-sum Games: Extra Gradient Succeeds where Optimism Fails

Last-iterate convergence has received extensive study in two player zero-sum games starting from bilinear, convex-concave up to settings that satisfy the MVI condition. Typical methods that exhibit last-iterate convergence for the aforementioned games include extra-gradient (EG) and optimistic gradient descent ascent (OGDA). However, all the established last-iterate convergence results hold for the restrictive setting where the underlying repeated game does not change over time. Recently, a line of research has focused on regret analysis of OGDA in time-varying games, i.e., games where payoffs evolve with time; the last-iterate behavior of OGDA and EG in time-varying environments remains unclear though. In this paper, we study the last-iterate behavior of various algorithms in two types of unconstrained, time-varying, bilinear zero-sum games: periodic and convergent perturbed games. These models expand upon the usual repeated game formulation and incorporate external environmental factors, such as the seasonal effects on species competition and vanishing external noise. In periodic games, we prove that EG will converge while OGDA and momentum method will diverge. This is quite surprising, as to the best of our knowledge, it is the first result that indicates EG and OGDA have qualitatively different last-iterate behaviors and do not exhibit similar behavior. In convergent perturbed games, we prove all these algorithms converge as long as the game itself stabilizes with a faster rate than $1/t$.

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arXiv2022

Stability of Decentralized Queueing Networks Beyond Complete Bipartite Cases

Gaitonde and Tardos recently studied a model of queueing networks where queues compete for servers and re-send returned packets in future rounds. They quantify the amount of additional processing power that guarantees a decentralized system's stability, both when the queues adapt their strategies from round to round using no-regret learning algorithms, and when they are patient and evaluate the utility of a strategy over long periods of time. In this paper, we generalize Gaitonde and Tardos's model and consider scenarios where not all servers can serve all queues (i.e., the underlying graph is an incomplete bipartite graphs) and, further, when packets need to go through more than one layer of servers before their completions (i.e., when the underlying graph is a DAG). For the bipartite case, we obtain bounds comparable to those by Gaitonde and Tardos, with the factor slightly worse in the patient queueing model. For the more general multi-layer systems, we show that straightforward generalizations of the utility function and servers' priority rules in Gaitonde and Tardos's model may lead to unbounded gaps between centralized and decentralized systems when the queues use no regret strategies. We define a new utility and a service priority rule that are aware of the queue lengths, and show that these suffice to restore the bounded gap between centralized and decentralized systems observed in bipartite graphs.

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arXiv2022

Pandora Box Problem with Nonobligatory Inspection: Hardness and Approximation Scheme

Weitzman (1979) introduced the Pandora Box problem as a model for sequential search with inspection costs, and gave an elegant index-based policy that attains provably optimal expected payoff. In various scenarios, the searching agent may select an option without making a costly inspection. The variant of the Pandora box problem with non-obligatory inspection has attracted interest from both economics and algorithms researchers. Various simple algorithms have proved suboptimal, with the best known 0.8-approximation algorithm due to Guha et al. (2008). No hardness result for the problem was known. In this work, we show that it is NP-hard to compute an optimal policy for Pandora's problem with nonobligatory inspection. We also give a polynomial-time approximation scheme (PTAS) that computes policies with an expected payoff at least $(1 - \epsilon)$-fraction of the optimal, for arbitrarily small $\epsilon > 0$. On the side, we show the decision version of the problem to be in NP.

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arXiv2021

Oblivious Online Contention Resolution Schemes

Contention resolution schemes (CRSs) are powerful tools for obtaining "ex post feasible" solutions from candidates that are drawn from "ex ante feasible" distributions. Online contention resolution schemes (OCRSs), the online version, have found myriad applications in Bayesian and stochastic problems, such as prophet inequalities and stochastic probing. When the ex ante distribution is unknown, it was unknown whether good CRSs/OCRSs exist with no sample (in which case the scheme is oblivious) or few samples from the distribution. In this work, we give a simple $\frac{1}{e}$-selectable oblivious single item OCRS by mixing two simple schemes evenly, and show, via a Ramsey theory argument, that it is optimal. On the negative side, we show that no CRS or OCRS with $O(1)$ samples can be $\Omega(1)$-balanced/selectable (i.e., preserve every active candidate with a constant probability) for graphic or transversal matroids.

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arXiv2020

Exponential Convergence of Gradient Methods in Concave Network Zero-sum Games

Motivated by Generative Adversarial Networks, we study the computation of Nash equilibrium in concave network zero-sum games (NZSGs), a multiplayer generalization of two-player zero-sum games first proposed with linear payoffs. Extending previous results, we show that various game theoretic properties of convex-concave two-player zero-sum games are preserved in this generalization. We then generalize last iterate convergence results obtained previously in two-player zero-sum games. We analyze convergence rates when players update their strategies using Gradient Ascent, and its variant, Optimistic Gradient Ascent, showing last iterate convergence in three settings -- when the payoffs of players are linear, strongly concave and Lipschitz, and strongly concave and smooth. We provide experimental results that support these theoretical findings.

cs.LG↗

arXiv2020

Learning Utilities and Equilibria in Non-Truthful Auctions

In non-truthful auctions, agents' utility for a strategy depends on the strategies of the opponents and also the prior distribution over their private types; the set of Bayes Nash equilibria generally has an intricate dependence on the prior. Using the First Price Auction as our main demonstrating example, we show that $\tilde O(n / \epsilon^2)$ samples from the prior with $n$ agents suffice for an algorithm to learn the interim utilities for all monotone bidding strategies. As a consequence, this number of samples suffice for learning all approximate equilibria. We give almost matching (up to polylog factors) lower bound on the sample complexity for learning utilities. We also consider a setting where agents must pay a search cost to discover their own types. Drawing on a connection between this setting and the first price auction, discovered recently by Kleinberg et al. (2016), we show that $\tilde O(n / \epsilon^2)$ samples suffice for utilities and equilibria to be estimated in a near welfare-optimal descending auction in this setting. En route, we improve the sample complexity bound, recently obtained by Guo et al. (2021), for the Pandora's Box problem, which is a classical model for sequential consumer search.

cs.GT↗

arXiv2020

Limitations of Incentive Compatibility on Discrete Type Spaces

In the design of incentive compatible mechanisms, a common approach is to enforce incentive compatibility as constraints in programs that optimize over feasible mechanisms. Such constraints are often imposed on sparsified representations of the type spaces, such as their discretizations or samples, in order for the program to be manageable. In this work, we explore limitations of this approach, by studying whether all dominant strategy incentive compatible mechanisms on a set $T$ of discrete types can be extended to the convex hull of $T$. Dobzinski, Fu and Kleinberg (2015) answered the question affirmatively for all settings where types are single dimensional. It is not difficult to show that the same holds when the set of feasible outcomes is downward closed. In this work we show that the question has a negative answer for certain non-downward-closed settings with multi-dimensional types. This result should call for caution in the use of the said approach to enforcing incentive compatibility beyond single-dimensional preferences and downward closed feasible outcomes.

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arXiv2019

Report-Sensitive Spot-Checking in Peer-Grading Systems

Peer grading systems make large courses more scalable, provide students with faster and more detailed feedback, and help students to learn by thinking critically about the work of others. A key obstacle to the broader adoption of peer grading systems is motivating students to provide accurate grades. The literature has explored many different approaches to incentivizing accurate grading (which we survey in detail), but the strongest incentive guarantees have been offered by mechanisms that compare peer grades to trusted TA grades with a fixed probability. In this work, we show that less TA work is required when these probabilities are allowed to depend on the grades that students report. We prove this result in a model with two possible grades, arbitrary numbers of agents, no requirement that students grade multiple assignments, arbitrary but homogeneous noisy observation of the ground truth which students can pay a fixed cost to observe, and the possibility of misreporting grades before or after observing this signal. We give necessary and sufficient conditions for our new mechanism's feasibility, prove its optimality under these assumptions, and characterize its improvement over the previous state of the art both analytically and empirically. Finally, we relax our homogeneity assumption, allowing each student and TA to observe the ground truth according to a different noise model.

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arXiv2019

The Vickrey Auction with a Single Duplicate Bidder Approximates the Optimal Revenue

Bulow and Klemperer's well-known result states that, in a single-item auction where the $n$ bidders' values are independently and identically drawn from a regular distribution, the Vickrey auction with one additional bidder (a duplicate) extracts at least as much revenue as the optimal auction without the duplicate. Hartline and Roughgarden, in their influential 2009 paper, removed the requirement that the distributions be identical, at the cost of allowing the Vickrey auction to recruit $n$ duplicates, one from each distribution, and relaxing its revenue advantage to a $2$-approximation. In this work we restore Bulow and Klemperer's number of duplicates in Hartline and Roughgarden's more general setting with a worse approximation ratio. We show that recruiting a duplicate from one of the distributions suffices for the Vickrey auction to $10$-approximate the optimal revenue. We also show that in a $k$-items unit demand auction, recruiting $k$ duplicates suffices for the VCG auction to $O(1)$-approximate the optimal revenue. As another result, we tighten the analysis for Hartline and Roughgarden's Vickrey auction with $n$ duplicates for the case with two bidders in the auction. We show that in this case the Vickrey auction with two duplicates obtains at least $3/4$ of the optimal revenue. This is tight by meeting a lower bound by Hartline and Roughgarden. En route, we obtain a transparent analysis of their $2$-approximation for $n$~bidders, via a natural connection to Ronen's lookahead auction.

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arXiv2019

Transparency and Control in Platforms for Networked Markets

In this paper, we analyze the worst case efficiency loss of online platform designs under a networked Cournot competition model. Inspired by some of the largest platforms in operation today, the platform designs that we consider examine the trade-off between transparency and control. Our results show that open access designs incentivize increased production towards perfectly competitive levels and limit efficiency loss, while controlled allocation designs lead to producer-platform incentive misalignment, resulting in low participation and unbounded efficiency loss. We also show that discriminatory access designs balance transparency and control, achieving the best of both worlds by maintaining high participation rates while limiting efficiency loss.

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arXiv2018

Third-Party Data Providers Ruin Simple Mechanisms

Motivated by the growing prominence of third-party data providers in online marketplaces, this paper studies the impact of the presence of third-party data providers on mechanism design. When no data provider is present, it has been shown that simple mechanisms are "good enough" -- they can achieve a constant fraction of the revenue of optimal mechanisms. The results in this paper demonstrate that this is no longer true in the presence of a third-party data provider who can provide the bidder with a signal that is correlated with the item type. Specifically, even with a single seller, a single bidder, and a single item of uncertain type for sale, the strategies of pricing each item-type separately (the analog of item pricing for multi-item auctions) and bundling all item-types under a single price (the analog of grand bundling) can both simultaneously be a logarithmic factor worse than the optimal revenue. Further, in the presence of a data provider, item-type partitioning mechanisms---a more general class of mechanisms which divide item-types into disjoint groups and offer prices for each group---still cannot achieve within a $\log \log$ factor of the optimal revenue. Thus, our results highlight that the presence of a data-provider forces the use of more complicated mechanisms in order to achieve a constant fraction of the optimal revenue.

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