Zero-Sum Stochastic Stackelberg Games

Zero-sum stochastic games have found important applications in a variety of fields, from machine learning to economics. Work on this model has primarily focused on the computation of Nash equilibrium due to its effectiveness in solving adversarial board and video games. Unfortunately, a Nash equilibrium is not guaranteed to exist in zero-sum stochastic games when the payoffs at each state are not convex-concave in the players' actions. A Stackelberg equilibrium, however, is guaranteed to exist. Consequently, in this paper, we study zero-sum stochastic Stackelberg games. Going beyond known existence results for (non-stationary) Stackelberg equilibria, we prove the existence of recursive (i.e., Markov perfect) Stackelberg equilibria (recSE) in these games, provide necessary and sufficient conditions for a policy profile to be a recSE, and show that recSE can be computed in (weakly) polynomial time via value iteration. Finally, we show that zero-sum stochastic Stackelberg games can model the problem of pricing and allocating goods across agents and time. More specifically, we propose a zero-sum stochastic Stackelberg game whose recSE correspond to the recursive competitive equilibria of a large class of stochastic Fisher markets. We close with a series of experiments that showcase how our methodology can be used to solve the consumption-savings problem in stochastic Fisher markets.Comment: 29 pages 2 figures, Appeared in NeurIPS'2

Thermal Effect of Metal Fin inside Elevated Radiant Floor Based on the Thermal Utilization of a Burning Cave

A rural house integrated with an elevated floor heating system based on the thermal utilization of a burning cave has been established to provide a more comfortable and clear indoor environment. Inside the elevated floor heating system, air is taken as the heat transfer medium and tin layer is designed as metal fin in the middle layer of the elevated floor to enhance heat transfer. In this study, heat transfer process and thermal performance of the inner metal fin were analyzed by theoretical calculations and field measurements. The results show that while the heat flux of the burning cave is decreased from 460 W/m2 to 200 W/m2, the convection heat intensity of the hot air inside the elevated floor under each room is from 2W/m2 to 9W/m2. Finally, it confirms that the effective length of the metal layer should be less than 0.4m. All the above results show that appropriate design parameters can lead to an optimum heat transfer process

Density-Based Region Search with Arbitrary Shape for Object Localization

Region search is widely used for object localization. Typically, the region search methods project the score of a classifier into an image plane, and then search the region with the maximal score. The recently proposed region search methods, such as efficient subwindow search and efficient region search, %which localize objects from the score distribution on an image are much more efficient than sliding window search. However, for some classifiers and tasks, the projected scores are nearly all positive, and hence maximizing the score of a region results in localizing nearly the entire images as objects, which is meaningless. In this paper, we observe that the large scores are mainly concentrated on or around objects. Based on this observation, we propose a method, named level set maximum-weight connected subgraph (LS-MWCS), which localizes objects with arbitrary shapes by searching regions with the densest score rather than the maximal score. The region density can be controlled by a parameter flexibly. And we prove an important property of the proposed LS-MWCS, which guarantees that the region with the densest score can be searched. Moreover, the LS-MWCS can be efficiently optimized by belief propagation. The method is evaluated on the problem of weakly-supervised object localization, and the quantitative results demonstrate the superiorities of our LS-MWCS compared to other state-of-the-art methods

Fisher Markets with Social Influence

A Fisher market is an economic model of buyer and seller interactions in which each buyer's utility depends only on the bundle of goods she obtains. Many people's interests, however, are affected by their social interactions with others. In this paper, we introduce a generalization of Fisher markets, namely influence Fisher markets, which captures the impact of social influence on buyers' utilities. We show that competitive equilibria in influence Fisher markets correspond to generalized Nash equilibria in an associated pseudo-game, which implies the existence of competitive equilibria in all influence Fisher markets with continuous and concave utility functions. We then construct a monotone pseudo-game, whose variational equilibria and their duals together characterize competitive equilibria in influence Fisher markets with continuous, jointly concave, and homogeneous utility functions. This observation implies that competitive equilibria in these markets can be computed in polynomial time under standard smoothness assumptions on the utility functions. The dual of this second pseudo-game enables us to interpret the competitive equilibria of influence CCH Fisher markets as the solutions to a system of simultaneous Stackelberg games. Finally, we derive a novel first-order method that solves this Stackelberg system in polynomial time, prove that it is equivalent to computing competitive equilibrium prices via t\^{a}tonnement, and run experiments that confirm our theoretical results

Parametric Instability in Long Optical Cavities and Suppression by Dynamic Transverse Mode Frequency Modulation

Three mode parametric instability has been predicted in Advanced gravitational wave detectors. Here we present the first observation of this phenomenon in a large scale suspended optical cavity designed to be comparable to those of advanced gravitational wave detectors. Our results show that previous modelling assumptions that transverse optical modes are stable in frequency except for frequency drifts on a thermal deformation time scale is unlikely to be valid for suspended mass optical cavities. We demonstrate that mirror figure errors cause a dependence of transverse mode offset frequency on spot position. Combined with low frequency residual motion of suspended mirrors, this leads to transverse mode frequency modulation which suppresses the effective parametric gain. We show that this gain suppression mechanism can be enhanced by laser spot dithering or fast thermal modulation. Using Advanced LIGO test mass data and thermal modelling we show that gain suppression factors of 10-20 could be achieved for individual modes, sufficient to greatly ameliorate the parametric instability problem