arXiv subjects

Song Zuo

Publications and source records attributed to Song Zuo.

28 records · Page 2Linked to original sources

arXiv2021

Automated Mechanism Design via Neural Networks

Using AI approaches to automatically design mechanisms has been a central research mission at the interface of AI and economics [Conitzer and Sandholm, 2002]. Previous approaches that attempt to design revenue optimal auctions for the multi-dimensional settings fall short in at least one of the three aspects: 1) representation -- search in a space that probably does not even contain the optimal mechanism; 2) exactness -- finding a mechanism that is either not truthful or far from optimal; 3) domain dependence -- need a different design for different environment settings. To resolve the three difficulties, in this paper, we put forward -- MenuNet -- a unified neural network based framework that automatically learns to design revenue optimal mechanisms. Our framework consists of a mechanism network that takes an input distribution for training and outputs a mechanism, as well as a buyer network that takes a mechanism as input and output an action. Such a separation in design mitigates the difficulty to impose incentive compatibility constraints on the mechanism, by making it a rational choice of the buyer. As a result, our framework easily overcomes the previously mentioned difficulty in incorporating IC constraints and always returns exactly incentive compatible mechanisms. We then apply our framework to a number of multi-item revenue optimal design settings, for a few of which the theoretically optimal mechanisms are unknown. We then go on to theoretically prove that the mechanisms found by our framework are indeed optimal. To the best of our knowledge, we are the first to apply neural networks to discover optimal auction mechanisms with provable optimality.

cs.AI↗

arXiv2021

Towards Efficient Auctions in an Auto-bidding World

Auto-bidding has become one of the main options for bidding in online advertisements, in which advertisers only need to specify high-level objectives and leave the complex task of bidding to auto-bidders. In this paper, we propose a family of auctions with boosts to improve welfare in auto-bidding environments with both return on ad spend constraints and budget constraints. Our empirical results validate our theoretical findings and show that both the welfare and revenue can be improved by selecting the weight of the boosts properly.

cs.GT↗

arXiv2019

Bayesian Nash Equilibrium in First-Price Auction with Discrete Value Distributions

First price auctions are widely used in government contracts and industrial auctions. In this paper, we consider the Bayesian Nash Equilibrium (BNE) in first price auctions with discrete value distributions. We study the characterization of the BNE in the first price auction and provide an algorithm to compute the BNE at the same time. Moreover, we prove the existence and the uniqueness of the BNE. Some of the previous results in the case of continuous value distributions do not apply to the case of discrete value distributions. In the meanwhile, the uniqueness result in discrete case cannot be implied by the uniqueness property in the continuous case. Unlike in the continuous case, we do not need to solve ordinary differential equations and thus do not suffer from the solution errors therein. Compared to the method of using continuous distributions to approximate discrete ones, our experiments show that our algorithm is both faster and more accurate. The results in this paper are derived in the asymmetric independent private values model, which assumes that the buyers' value distributions are common knowledge.

cs.GT↗

arXiv2019

The Matthew Effect in Computation Contests: High Difficulty May Lead to 51% Dominance

We study the computation contests where players compete for searching a solution to a given problem with a winner-take-all reward. The search processes are independent across the players and the search speeds of players are proportional to their computational powers. One concrete application of this abstract model is the mining process of proof-of-work type blockchain systems, such as Bitcoin. Although one's winning probability is believed to be proportional to his computational power in previous studies on Bitcoin, we show that it is not the case in the strict sense. Because of the gaps between the winning probabilities and the proportions of computational powers, the Matthew effect will emerge in the system, where the rich get richer and the poor get poorer. In addition, we show that allowing the players to pool with each other or reducing the number of solutions to the problem may aggravate the Matthew effect and vice versa.

cs.GT↗

arXiv2018

Optimal Dynamic Auctions are Virtual Welfare Maximizers

We are interested in the setting where a seller sells sequentially arriving items, one per period, via a dynamic auction. At the beginning of each period, each buyer draws a private valuation for the item to be sold in that period and this valuation is independent across buyers and periods. The auction can be dynamic in the sense that the auction at period $t$ can be conditional on the bids in that period and all previous periods, subject to certain appropriately defined incentive compatible and individually rational conditions. Perhaps not surprisingly, the revenue optimal dynamic auctions are computationally hard to find and existing literatures that aim to approximate the optimal auctions are all based on solving complex dynamic programs. It remains largely open on the structural interpretability of the optimal dynamic auctions. In this paper, we show that any optimal dynamic auction is a virtual welfare maximizer subject to some monotone allocation constraints. In particular, the explicit definition of the virtual value function above arises naturally from the primal-dual analysis by relaxing the monotone constraints. We further develop an ironing technique that gets rid of the monotone allocation constraints. Quite different from Myerson's ironing approach, our technique is more technically involved due to the interdependence of the virtual value functions across buyers. We nevertheless show that ironing can be done approximately and efficiently, which in turn leads to a Fully Polynomial Time Approximation Scheme of the optimal dynamic auction.

cs.GT↗

arXiv2018

Optimal Vehicle Dispatching Schemes via Dynamic Pricing

Over the past few years, ride-sharing has emerged as an effective way to relieve traffic congestion. A key problem for these platforms is to come up with a revenue-optimal (or GMV-optimal) pricing scheme and an induced vehicle dispatching policy that incorporate geographic and temporal information. In this paper, we aim to tackle this problem via an economic approach. Modeled naively, the underlying optimization problem may be non-convex and thus hard to compute. To this end, we use a so-called "ironing" technique to convert the problem into an equivalent convex optimization one via a clean Markov decision process (MDP) formulation, where the states are the driver distributions and the decision variables are the prices for each pair of locations. Our main finding is an efficient algorithm that computes the exact revenue-optimal (or GMV-optimal) randomized pricing schemes. We characterize the optimal solution of the MDP by a primal-dual analysis of a corresponding convex program. We also conduct empirical evaluations of our solution through real data of a major ride-sharing platform and show its advantages over fixed pricing schemes as well as several prevalent surge-based pricing schemes.

eess.SY↗

arXiv2017

Generalizing Virtual Values to Multidimensional Auctions: a Non-Myersonian Approach

We consider the revenue maximization problem of a monopolist via a non-Myersonian approach that could generalize to multiple items and multiple buyers. Although such an approach does not lead to any closed-form solution of the problem, it does provide some insights into this problem from different angles. In particular, we consider both Bayesian (Bayesian Incentive Compatible + Bayesian Individually Rational) and Dominant-Strategy (Dominant-Strategy Incentive Compatible + ex-post Individually Rational) implementations, where all the buyers have additive valuations and quasi-linear utilities and all the valuations are independent across buyers (not necessarily independent across items). The main technique of our approach is to formulate the problem as an LP (probably with exponential size) and apply primal-dual analysis. We observe that any optimal solution of the dual program naturally defines the virtual value functions for the primal revenue maximization problem in the sense that any revenue-maximizing auction must be a virtual welfare maximizer (cf. Myerson's auction for a single item [Myerson, 1981]). Based on this observation, we characterize a sufficient and necessary condition for BIC = DSIC, i.e., the optimal revenue of Bayesian implementations equals to the optimal revenue of dominant-strategy implementations (BRev = DRev). The condition is if and only if the optimal DSIC revenue DRev can be achieved by a DSIC and ex-post IR virtual welfare maximizer with buyer-independent virtual value functions (buyer i's virtual value is independent of other buyers' valuations). In light of the characterization, we further show that when all the valuations are i.i.d., it is further equivalent to that separate-selling is optimal. In particular, it respects one result from the recent breakthrough work on the exact optimal solutions in the multi-item multi-buyer setting by Yao [2016].

cs.GT↗

arXiv2016

Optimal dynamic mechanisms with ex-post IR via bank accounts

Lately, the problem of designing multi-stage dynamic mechanisms has been shown to be both theoretically challenging and practically important. In this paper, we consider the problem of designing revenue optimal dynamic mechanism for a setting where an auctioneer sells a set of items to a buyer in multiple stages. At each stage, there could be multiple items for sale but each item can only appear in one stage. The type of the buyer at each stage is thus a multi-dimensional vector characterizing the buyer's valuations of the items at that stage and is assumed to be stage-wise independent. In particular, we propose a novel class of mechanisms called bank account mechanisms. Roughly, a bank account mechanism is no different from any stage-wise individual mechanism except for an augmented structure called bank account, a real number for each node that summarizes the history so far. We first establish that the optimal revenue from any dynamic mechanism in this setting can be achieved by a bank account mechanism, and we provide a simple characterization of the set of incentive compatible and ex-post individually rational bank account mechanisms. Based on these characterizations, we then investigate the problem of finding the (approximately) optimal bank account mechanisms. We prove that there exists a simple, randomized bank account mechanism that approximates optimal revenue up to a constant factor. Our result is general and can accommodate previous approximation results in single-shot multi-dimensional mechanism design. Based on the previous mechanism, we further show that there exists a deterministic bank account mechanism that achieves constant-factor approximation as well. Finally, we consider the problem of computing optimal mechanisms when the type space is discrete and provide an FPTAS via linear and dynamic programming.

cs.GT↗

arXiv2014

Tighter Relations Between Sensitivity and Other Complexity Measures

Sensitivity conjecture is a longstanding and fundamental open problem in the area of complexity measures of Boolean functions and decision tree complexity. The conjecture postulates that the maximum sensitivity of a Boolean function is polynomially related to other major complexity measures. Despite much attention to the problem and major advances in analysis of Boolean functions in the past decade, the problem remains wide open with no positive result toward the conjecture since the work of Kenyon and Kutin from 2004. In this work, we present new upper bounds for various complexity measures in terms of sensitivity improving the bounds provided by Kenyon and Kutin. Specifically, we show that deg(f)^{1-o(1)}=O(2^{s(f)}) and C(f) < 2^{s(f)-1} s(f); these in turn imply various corollaries regarding the relation between sensitivity and other complexity measures, such as block sensitivity, via known results. The gap between sensitivity and other complexity measures remains exponential but these results are the first improvement for this difficult problem that has been achieved in a decade.

cs.CC↗

arXiv2013

New upper bound on block sensitivity and certificate complexity in terms of sensitivity

Sensitivity \cite{CD82,CDR86} and block sensitivity \cite{Nisan91} are two important complexity measures of Boolean functions. A longstanding open problem in decision tree complexity, the "Sensitivity versus Block Sensitivity" question, proposed by Nisan and Szegedy \cite{Nisan94} in 1992, is whether these two complexity measures are polynomially related, i.e., whether $bs(f)=O(s(f)^{O(1)})$. We prove an new upper bound on block sensitivity in terms of sensitivity: $bs(f) \leq 2^{s(f)-1} s(f)$. Previously, the best upper bound on block sensitivity was $bs(f) \leq (\frac{e}{\sqrt{2π}}) e^{s(f)} \sqrt{s(f)}$ by Kenyon and Kutin \cite{KK}. We also prove that if $\min\{s_0(f),s_1(f)\}$ is a constant, then sensitivity and block sensitivity are linearly related, i.e. $bs(f)=O(s(f))$.

cs.CC↗