186 research outputs found
On Unconstrained Quasi-Submodular Function Optimization
With the extensive application of submodularity, its generalizations are
constantly being proposed. However, most of them are tailored for special
problems. In this paper, we focus on quasi-submodularity, a universal
generalization, which satisfies weaker properties than submodularity but still
enjoys favorable performance in optimization. Similar to the diminishing return
property of submodularity, we first define a corresponding property called the
{\em single sub-crossing}, then we propose two algorithms for unconstrained
quasi-submodular function minimization and maximization, respectively. The
proposed algorithms return the reduced lattices in iterations,
and guarantee the objective function values are strictly monotonically
increased or decreased after each iteration. Moreover, any local and global
optima are definitely contained in the reduced lattices. Experimental results
verify the effectiveness and efficiency of the proposed algorithms on lattice
reduction.Comment: 11 page
A Utility-Theoretic Approach to Privacy in Online Services
Online offerings such as web search, news portals, and e-commerce applications face the challenge of providing high-quality service to a large, heterogeneous user base. Recent efforts have highlighted the potential to improve performance by introducing methods to personalize services based on special knowledge about users and their context. For example, a user's demographics, location, and past search and browsing may be useful in enhancing the results offered in response to web search queries. However, reasonable concerns about privacy by both users, providers, and government agencies acting on behalf of citizens, may limit access by services to such information. We introduce and explore an economics of privacy in personalization, where people can opt to share personal information, in a standing or on-demand manner, in return for expected enhancements in the quality of an online service. We focus on the example of web search and formulate realistic objective functions for search efficacy and privacy. We demonstrate how we can find a provably near-optimal optimization of the utility-privacy tradeoff in an efficient manner. We evaluate our methodology on data drawn from a log of the search activity of volunteer participants. We separately assess usersâ preferences about privacy and utility via a large-scale survey, aimed at eliciting preferences about peoplesâ willingness to trade the sharing of personal data in returns for gains in search efficiency. We show that a significant level of personalization can be achieved using a relatively small amount of information about users
Supermodular mechanism design
This paper introduces a mechanism design approach that allows dealing with the multiple equilibrium problem, using mechanisms that are robust to bounded rationality. This approach is a tool for constructing supermodular mechanisms, i.e. mechanisms that induce games with strategic complementarities. In quasilinear environments, I prove that if a social choice function can be implemented by a mechanism that generates bounded strategic substitutes - as opposed to strategic complementarities - then this mechanism can be converted into a supermodular mechanism that implements the social choice function. If the social choice function also satisfies some efficiency criterion, then it admits a supermodular mechanism that balances the budget. Building on these results, I address the multiple equilibrium problem. I provide sufficient conditions for a social choice function to be implementable with a supermodular mechanism whose equilibria are contained in the smallest interval among all supermodular mechanisms. This is followed by conditions for supermodular implementability in unique equilibrium. Finally, I provide a revelation principle for supermodular implementation in environments with general preferences.Implementation, mechanisms, learning, strategic complementarities, supermodular games
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Fair Robust Assignment Using Redundancy
We study the consideration of fairness in redundant assignment for multi-agent task allocation. It has recently been shown that redundant assignment of agents to tasks provides robustness to uncertainty in task performance. However, the question of how to fairly assign these redundant resources across tasks remains unaddressed. In this paper, we present a novel problem formulation for fair redundant task allocation, in which we cast it as the optimization of worst-case task costs. Solving this problem optimally is NP-hard. Therefore, we exploit properties of supermodularity to propose a polynomial-time, near-optimal solution. Our algorithm provides a solution set that is α times larger than the optimal set size in order to guarantee a solution cost at least as good as the optimal target cost. We derive the sub- optimality bound on this cardinality relaxation, α. Additionally, we demonstrate that our algorithm performs near-optimally without the cardinality relaxation. We show the algorithm in simulations of redundant assignments of robots to goal nodes on transport networks with uncertain travel times. Empirically, our algorithm outperforms benchmarks, scales to large problems, and provides improvements in both fairness and average utility.We gratefully acknowledge the support from ARL Grant DCIST CRA W911NF-17-2-0181, NSF Grant CNS-1521617, ARO Grant W911NF-13-1- 0350, ONR Grants N00014-20-1-2822 and ONR grant N00014-20-S-B001, and Qualcomm Research. The first author acknowledges support from the National Science Foundation Graduate Research Fellowship under Grant No. DGE-1845298
Fair Robust Assignment Using Redundancy
We study the consideration of fairness in redundant assignment for multi-agent task allocation. It has recently been shown that redundant assignment of agents to tasks provides robustness to uncertainty in task performance. However, the question of how to fairly assign these redundant resources across tasks remains unaddressed. In this paper, we present a novel problem formulation for fair redundant task allocation, in which we cast it as the optimization of worst-case task costs. Solving this problem optimally is NP-hard. Therefore, we exploit properties of supermodularity to propose a polynomial-time, near-optimal solution. Our algorithm provides a solution set that is α times larger than the optimal set size in order to guarantee a solution cost at least as good as the optimal target cost. We derive the sub- optimality bound on this cardinality relaxation, α. Additionally, we demonstrate that our algorithm performs near-optimally without the cardinality relaxation. We show the algorithm in simulations of redundant assignments of robots to goal nodes on transport networks with uncertain travel times. Empirically, our algorithm outperforms benchmarks, scales to large problems, and provides improvements in both fairness and average utility.We gratefully acknowledge the support from ARL Grant DCIST CRA W911NF-17-2-0181, NSF Grant CNS-1521617, ARO Grant W911NF-13-1- 0350, ONR Grants N00014-20-1-2822 and ONR grant N00014-20-S-B001, and Qualcomm Research. The first author acknowledges support from the National Science Foundation Graduate Research Fellowship under Grant No. DGE-1845298
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