A convergence analysis of the price of anarchy in atomic congestion games
This paper provides a comprehensive convergence analysis of the PoA of both pure and mixed Nash equilibria in atomic congestion games with unsplittable demands.
cs.GT↗
arXiv subjects
Zijun Wu
Publications and source records attributed to Zijun Wu.
GridDehazeNet+: An Enhanced Multi-Scale Network with Intra-Task Knowledge Transfer for Single Image Dehazing
We propose an enhanced multi-scale network, dubbed GridDehazeNet+, for single image dehazing. The proposed dehazing method does not rely on the Atmosphere Scattering Model (ASM), and an explanation as to why it is not necessarily performing the dimension reduction offered by this model is provided. GridDehazeNet+ consists of three modules: pre-processing, backbone, and post-processing. The trainable pre-processing module can generate learned inputs with better diversity and more pertinent features as compared to those derived inputs produced by hand-selected pre-processing methods. The backbone module implements multi-scale estimation with two major enhancements: 1) a novel grid structure that effectively alleviates the bottleneck issue via dense connections across different scales; 2) a spatial-channel attention block that can facilitate adaptive fusion by consolidating dehazing-relevant features. The post-processing module helps to reduce the artifacts in the final output. Due to domain shift, the model trained on synthetic data may not generalize well on real data. To address this issue, we shape the distribution of synthetic data to match that of real data, and use the resulting translated data to finetune our network. We also propose a novel intra-task knowledge transfer mechanism that can memorize and take advantage of synthetic domain knowledge to assist the learning process on the translated data. Experimental results demonstrate that the proposed method outperforms the state-of-the-art on several synthetic dehazing datasets, and achieves the superior performance on real-world hazy images after finetuning.
cs.CV↗
A sensitivity analysis for the price of anarchy in non-atomic congestion games
This paper shows that the PoA in non-atomic congestion games is H{ö}lder continuous w.r.t. combined disturbance on cost functions and demands. We then apply this result to the convergence analysis of the PoA.
cs.GT↗
An Improved Generic Bet-and-Run Strategy for Speeding Up Stochastic Local Search
A commonly used strategy for improving optimization algorithms is to restart the algorithm when it is believed to be trapped in an inferior part of the search space. Building on the recent success of Bet-and-Run approaches for restarted local search solvers, we introduce an improved generic Bet-and-Run strategy. The goal is to obtain the best possible results within a given time budget t using a given black-box optimization algorithm. If no prior knowledge about problem features and algorithm behavior is available, the question about how to use the time budget most efficiently arises. We propose to first start k>=1 independent runs of the algorithm during an initialization budget t1 =0 time units in doing so), and then continuing these runs for the remaining t3=t-t1-t2 time units. In previous Bet-and-Run strategies, the decision maker D=currentBest would simply select the run with the best- so-far results at negligible time. We propose using more advanced methods to discriminate between "good" and "bad" sample runs, with the goal of increasing the correlation of the chosen run with the a-posteriori best one. We test several different approaches, including neural networks trained or polynomials fitted on the current trace of the algorithm to predict which run may yield the best results if granted the remaining budget. We show with extensive experiments that this approach can yield better results than the previous methods, but also find that the currentBest method is a very reliable and robust baseline approach.
cs.NE↗
Selfishness need not be bad: a general proof
This article studies the user behavior in non-atomic congestion games. We consider non-atomic congestion games with continuous and non-decreasing functions and investigate the limit of the price of anarchy when the total user volume approaches infinity. We deepen the knowledge on {\em asymptotically well designed games} \cite{Wu2017Selfishness}, {\em limit games} \cite{Wu2017Selfishness}, {\em scalability} \cite{Wu2017Selfishness} and {\em gaugeability} \cite{Colini2017b} that were recently used in the limit analyses of the price of anarchy for non-atomic congestion games. We develop a unified framework and derive new techniques that allow a general limit analysis of the price of anarchy. With these new techniques, we are able to prove a global convergence on the price of anarchy for non-atomic congestion games with arbitrary polynomial price functions and arbitrary user volume vector sequences. Moreover, we show that these new techniques are very flexible and robust and apply also to non-atomic congestion games with price functions of other types. In particular, we prove that non-atomic congestion games with regularly varying price functions are also asymptotically well designed, provided that the price functions are slightly restricted. Our results greatly generalize recent results. In particular, our results further support the view with a general proof that selfishness need not be bad for non-atomic congestion games.
cs.GT↗
Stochastic Runtime Analysis of a Cross Entropy Algorithm for Traveling Salesman Problems
This article analyzes the stochastic runtime of a Cross-Entropy Algorithm on two classes of traveling salesman problems. The algorithm shares main features of the famous Max-Min Ant System with iteration-best reinforcement. For simple instances that have a $\{1,n\}$-valued distance function and a unique optimal solution, we prove a stochastic runtime of $O(n^{6+ε})$ with the vertex-based random solution generation, and a stochastic runtime of $O(n^{3+ε}\ln n)$ with the edge-based random solution generation for an arbitrary $ε\in (0,1)$. These runtimes are very close to the known expected runtime for variants of Max-Min Ant System with best-so-far reinforcement. They are obtained for the stronger notion of stochastic runtime, which means that an optimal solution is obtained in that time with an overwhelming probability, i.e., a probability tending exponentially fast to one with growing problem size. We also inspect more complex instances with $n$ vertices positioned on an $m\times m$ grid. When the $n$ vertices span a convex polygon, we obtain a stochastic runtime of $O(n^{3}m^{5+ε})$ with the vertex-based random solution generation, and a stochastic runtime of $O(n^{2}m^{5+ε})$ for the edge-based random solution generation. When there are $k = O(1)$ many vertices inside a convex polygon spanned by the other $n-k$ vertices, we obtain a stochastic runtime of $O(n^{4}m^{5+ε}+n^{6k-1}m^ε)$ with the vertex-based random solution generation, and a stochastic runtime of $O(n^{3}m^{5+ε}+n^{3k}m^ε)$ with the edge-based random solution generation. These runtimes are better than the expected runtime for the so-called $(μ\!+\!λ)$ EA reported in a recent article, and again obtained for the stronger notion of stochastic runtime.
cs.DS↗
Improving the Quality of Random Number Generators by Applying a Simple Ratio Transformation
It is well-known that the quality of random number generators can often be improved by combining several generators, e.g. by summing or subtracting their results. In this paper we investigate the ratio of two random number generators as an alternative approach: the smaller of two input random numbers is divided by the larger, resulting in a rational number from $[0,1]$. We investigate theoretical properties of this approach and show that it yields a good approximation to the ideal uniform distribution. To evaluate the empirical properties we use the well-known test suite \textsc{TestU01}. We apply the ratio transformation to moderately bad generators, i.e. those that failed up to 40\% of the tests from the test battery \textsc{Crush} of \textsc{TestU01}. We show that more than half of them turn into very good generators that pass all tests of \textsc{Crush} and \textsc{BigCrush} from \textsc{TestU01} when the ratio transformation is applied. In particular, generators based on linear operations seem to benefit from the ratio, as this breaks up some of the unwanted regularities in the input sequences. Thus the additional effort to produce a second random number and to calculate the ratio allows to increase the quality of available random number generators.
cs.OH↗