The Nash social welfare problem asks for an allocation of indivisible items to agents in order to maximize the geometric mean of agents' valuations. We give an overview of the constant-factor approximation algorithm for the problem when agents have Rado valuations [Garg et al. 2021]. Rado valuations are a common generalization of the assignment (OXS) valuations and weighted matroid rank functions. Our approach also gives the first constant-factor approximation algorithm for the asymmetric Nash social welfare problem under the same valuations, provided that the maximum ratio between the weights is bounded by a constant.
more »
« less
utomating Mechanism Design with Program Synthesis
This paper presents a new approach to the automated design of mechanisms that incentivize self-interested agents to maximize a global objective (such as revenue or social welfare) in equilibrium. Prior work on automated design has either been restricted to relatively simple mechanisms, or represented mechanisms as neural networks that are hard to interpret and cannot easily incorporate prior knowledge. In this paper, we propose program synthesis as a way around these issues. Concretely, we formalize the problem of designing mechanisms in the form of multiagent environments whose transition and reward functions are programs in a domainspecific language (DSL), in order to maximize an outcome such as revenue or social welfare under given assumptions on how agents act in these environments. We present an initial algorithm, based on a combination of stochastic search over programs and Bayesian optimization, for this problem. We empirically evaluate the algorithm in two domains with different characteristics. Our experiments suggest that the approach can synthesize programmatic mechanisms that are human-interpretable and also perform well.
more »
« less
- Award ID(s):
- 1704883
- NSF-PAR ID:
- 10391908
- Date Published:
- Journal Name:
- Proc. Automated Learning Agents Workshop
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
More Like this
-
-
We consider information design in spatial resource competition, motivated by ride sharing platforms sharing information with drivers about rider demand. Each of N co-located agents (drivers) decides whether to move to another location with an uncertain and possibly higher resource level (rider demand), where the utility for moving increases in the resource level and decreases in the number of other agents that move. A principal who can observe the resource level wishes to share this information in a way that ensures a welfare-maximizing number of agents move. Analyzing the principal’s information design problem using the Bayesian persuasion framework, we study both private signaling mechanisms, where the principal sends personalized signals to each agent, and public signaling mechanisms, where the principal sends the same information to all agents. We show: 1) For private signaling, computing the optimal mechanism using the standard approach leads to a linear program with 2 N variables, rendering the computation challenging. We instead describe a computationally efficient two-step approach to finding the optimal private signaling mechanism. First, we perform a change of variables to solve a linear program with O(N^2) variables that provides the marginal probabilities of recommending each agent move. Second, we describe an efficient sampling procedure over sets of agents consistent with these optimal marginal probabilities; the optimal private mechanism then asks the sampled set of agents to move and the rest to stay. 2) For public signaling, we first show the welfare-maximizing equilibrium given any common belief has a threshold structure. Using this, we show that the optimal public mechanism with respect to the sender-preferred equilibrium can be computed in polynomial time. 3) We support our analytical results with numerical computations that show the optimal private and public signaling mechanisms achieve substantially higher social welfare when compared with no-information and full-information benchmarks.more » « less
-
Dimensionality reduction is a classical technique widely used for data analysis. One foundational instantiation is Principal Component Analysis (PCA), which minimizes the average reconstruction error. In this paper, we introduce the multi-criteria dimensionality reduction problem where we are given multiple objectives that need to be optimized simultaneously. As an application, our model captures several fairness criteria for dimensionality reduction such as the Fair-PCA problem introduced by Samadi et al. [NeurIPS18] and the Nash Social Welfare (NSW) problem. In the Fair-PCA problem, the input data is divided into k groups, and the goal is to find a single d-dimensional representation for all groups for which the maximum reconstruction error of any one group is minimized. In NSW the goal is to maximize the product of the individual variances of the groups achieved by the common low-dimensinal space. Our main result is an exact polynomial-time algorithm for the two-criteria dimensionality reduction problem when the two criteria are increasing concave functions. As an application of this result, we obtain a polynomial time algorithm for Fair-PCA for k=2 groups, resolving an open problem of Samadi et al.[NeurIPS18], and a polynomial time algorithm for NSW objective for k=2 groups. We also give approximation algorithms for k>2. Our technical contribution in the above results is to prove new low-rank properties of extreme point solutions to semi-definite programs. We conclude with the results of several experiments indicating improved performance and generalized application of our algorithm on real-world datasets.more » « less
-
null (Ed.)Dimensionality reduction is a classical technique widely used for data analysis. One foundational instantiation is Principal Component Analysis (PCA), which minimizes the average reconstruction error. In this paper, we introduce the multi-criteria dimensionality reduction problem where we are given multiple objectives that need to be optimized simultaneously. As an application, our model captures several fairness criteria for dimensionality reduction such as the Fair-PCA problem introduced by Samadi et al. [NeurIPS18] and the Nash Social Welfare (NSW) problem. In the Fair-PCA problem, the input data is divided into k groups, and the goal is to find a single d-dimensional representation for all groups for which the maximum reconstruction error of any one group is minimized. In NSW the goal is to maximize the product of the individual variances of the groups achieved by the common low-dimensinal space.more » « less
Our main result is an exact polynomial-time algorithm for the two-criteria dimensionality reduction problem when the two criteria are increasing concave functions. As an application of this result, we obtain a polynomial time algorithm for Fair-PCA for k=2 groups, resolving an open problem of Samadi et al.[NeurIPS18], and a polynomial time algorithm for NSW objective for k=2 groups. We also give approximation algorithms for k>2. Our technical contribution in the above results is to prove new low-rank properties of extreme point solutions to semi-definite programs. We conclude with the results of several experiments indicating improved performance and generalized application of our algorithm on real-world datasets.
-
Integration of distributed renewable energy sources (D- RES) has been introduced as a viable solution to offer cheap and clean energy to customers in decentralized power system. D- RES can offer local generation to flexible customers based on their servicing deadline and constraints, benefiting both D- RES owners and customers in terms of providing economic revenue and reducing the cost of supplied energy. In this context, this paper proposes a dynamic matching framework using model predictive control (MPC) to enable local energy sharing in power system operation. The proposed matching framework matches flexible customers with D- RES to maximize social welfare in the matching market, while meeting the customers' servicing constraints prior to their deadline. Simulations are conducted on a test power system using multiple matching algorithms across different load and generation scenarios and the results highlighted the efficiency of proposed framework in matching flexible customers with the appropriate supply sources to maximize social welfare in the matching market.more » « less
- Free Publicly Accessible Full Text
-
Accepted Manuscript1.0
- Conference Paper:
- The DOI is not currently available.
