arXiv subjects

Zongjun Yang

Publications and source records attributed to Zongjun Yang.

6 recordsLinked to original sources

arXiv2026

Competitive Equilibrium in Labor Economies through the Lens of Goods and Chores Fisher Markets

In this paper, we study a two-sided labor market that couples the classical Fisher market with goods and the Fisher market with bads into a single unified framework. In our model, users demand tasks in order to derive utility, while workers supply labor to perform these tasks in exchange for earnings. Each task thus plays a dual role: it is a good for the user side of the market and a chore for the worker side. Given prices for tasks, users choose utility-maximizing bundles subject to budgets, while workers choose disutility-minimizing task bundles subject to earning requirements; the resulting choices induce demand and supply endogenously for each task, and a CE corresponds to prices at which these coincide. We show that such markets are guaranteed to admit a CE in a very general setting, and the first and second welfare theorems hold for our labor market model. We next study the computation of equilibria under linear preferences. We show that, similar to the chores setting, equilibria correspond to KKT points of an Eisenberg-Gale-like non-convex program. Despite the non-convex characterization, we go on to show a set of surprisingly positive results. First, we show that there exists a polynomial-time combinatorial algorithm for computing CE, which relies on a natural Walrasian scheme for updating prices. In the "CEEI-like" case, this yields a strongly polynomial-time algorithm. We next show that our market admits a natural dual program, and this non-convex labor-market program admits a change of variables that transforms it into a linear program (albeit with irrational coefficients). Finally, leveraging this LP, we give yet another polynomial-time algorithm while deriving an approach for addressing the irrational coefficients in an efficient manner. We note that, even for goods-only linear Fisher markets, obtaining such an LP formulation remains open.

cs.GT↗

arXiv2026

Online Generalized-mean Welfare Maximization: Achieving Near-Optimal Regret from Samples

We study online fair allocation of $T$ sequentially arriving items among $n$ agents with heterogeneous preferences, with the objective of maximizing generalized-mean welfare, defined as the $p$-mean of agents' time-averaged utilities, with $p\in (-\infty, 1)$. We first consider the i.i.d. arrival model and show that the pure greedy algorithm -- which myopically chooses the welfare-maximizing integral allocation -- achieves $\widetilde{O}(1/T)$ average regret. Importantly, in contrast to prior work, our algorithm does not require distributional knowledge and achieves the optimal regret rate using only the online samples. We then go beyond i.i.d. arrivals and investigate a nonstationary model with time-varying independent distributions. In the absence of additional data about the distributions, it is known that every online algorithm must suffer $\Omega(1)$ average regret. We show that only a single historical sample from each distribution is sufficient to recover the optimal $\widetilde{O}(1/T)$ average regret rate, even in the face of arbitrary non-stationarity. Our algorithms are based on the re-solving paradigm: they assume that the remaining items will be the ones seen historically in those periods and solve the resulting welfare-maximization problem to determine the decision in every period. Finally, we also account for distribution shifts that may distort the fidelity of historical samples and show that the performance of our re-solving algorithms is robust to such shifts.

cs.GT↗

arXiv2024

Online Fair Allocation with Best-of-Many-Worlds Guarantees

We investigate the online fair allocation problem with sequentially arriving items under various input models, with the goal of balancing fairness and efficiency. We propose the unconstrained PACE (Pacing According to Current Estimated utility) algorithm, a parameter-free allocation dynamic that requires no prior knowledge of the input while using only integral allocations. PACE attains near-optimal convergence or approximation guarantees under stationary, stochastic-but-nonstationary, and adversarial input types, thereby achieving the first best-of-many-worlds guarantee in online fair allocation. Beyond theoretical bounds, PACE is highly simple, efficient, and decentralized, and is thus likely to perform well on a broad range of real-world inputs. Numerical results support the conclusion that PACE works well under a variety of input models. We find that PACE performs very well on two real-world datasets even under the true temporal arrivals in the data, which are highly nonstationary.

cs.GT↗

arXiv2023

Learning against Non-credible Auctions

The standard framework of online bidding algorithm design assumes that the seller commits himself to faithfully implementing the rules of the adopted auction. However, the seller may attempt to cheat in execution to increase his revenue if the auction belongs to the class of non-credible auctions. For example, in a second-price auction, the seller could create a fake bid between the highest bid and the second highest bid. This paper focuses on one such case of online bidding in repeated second-price auctions. At each time $t$, the winner with bid $b_t$ is charged not the highest competing bid $d_t$ but a manipulated price $p_t = \alpha_0 d_t + (1-\alpha_0) b_t$, where the parameter $\alpha_0 \in [0, 1]$ in essence measures the seller's credibility. Unlike classic repeated-auction settings where the bidder has access to samples $(d_s)_{s=1}^{t-1}$, she can only receive mixed signals of $(b_s)_{s=1}^{t-1}$, $(d_s)_{s=1}^{t-1}$ and $\alpha_0$ in this problem. The task for the bidder is to learn not only the bid distributions of her competitors but also the seller's credibility. We establish regret lower bounds in various information models and provide corresponding online bidding algorithms that can achieve near-optimal performance. Specifically, we consider three cases of prior information based on whether the credibility $\alpha_0$ and the distribution of the highest competing bids are known. Our goal is to characterize the landscape of online bidding in non-credible auctions and understand the impact of the seller's credibility on online bidding algorithm design under different information structures.

cs.GT↗

arXiv2023

Greedy-Based Online Fair Allocation with Adversarial Input: Enabling Best-of-Many-Worlds Guarantees

We study an online allocation problem with sequentially arriving items and adversarially chosen agent values, with the goal of balancing fairness and efficiency. Our goal is to study the performance of algorithms that achieve strong guarantees under other input models such as stochastic inputs, in order to achieve robust guarantees against a variety of inputs. To that end, we study the PACE (Pacing According to Current Estimated utility) algorithm, an existing algorithm designed for stochastic input. We show that in the equal-budgets case, PACE is equivalent to the integral greedy algorithm. We go on to show that with natural restrictions on the adversarial input model, both integral greedy allocation and PACE have asymptotically bounded multiplicative envy as well as competitive ratio for Nash welfare, with the multiplicative factors either constant or with optimal order dependence on the number of agents. This completes a "best-of-many-worlds" guarantee for PACE, since past work showed that PACE achieves guarantees for stationary and stochastic-but-non-stationary input models.

cs.GT↗

arXiv2023

Learning to Bid in Repeated First-Price Auctions with Budgets

Budget management strategies in repeated auctions have received growing attention in online advertising markets. However, previous work on budget management in online bidding mainly focused on second-price auctions. The rapid shift from second-price auctions to first-price auctions for online ads in recent years has motivated the challenging question of how to bid in repeated first-price auctions while controlling budgets. In this work, we study the problem of learning in repeated first-price auctions with budgets. We design a dual-based algorithm that can achieve a near-optimal $\widetilde{O}(\sqrt{T})$ regret with full information feedback where the maximum competing bid is always revealed after each auction. We further consider the setting with one-sided information feedback where only the winning bid is revealed after each auction. We show that our modified algorithm can still achieve an $\widetilde{O}(\sqrt{T})$ regret with mild assumptions on the bidder's value distribution. Finally, we complement the theoretical results with numerical experiments to confirm the effectiveness of our budget management policy.

cs.GT↗