Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userValue Variance Minimization for Learning Approximate Equilibrium in Aggregation Systems
67
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
For effective matching of resources (e.g., taxis, food, bikes, shopping items) to customer demand, aggregation systems have been extremely successful. In aggregation systems, a central entity (e.g., Uber, Food Panda, Ofo) aggregates supply (e.g., drivers, delivery personnel) and matches demand to supply on a continuous basis (sequential decisions). Due to the objective of the central entity to maximize its profits, individual suppliers get sacrificed thereby creating incentive for individuals to leave the system. In this paper, we consider the problem of learning approximate equilibrium solutions (win-win solutions) in aggregation systems, so that individuals have an incentive to remain in the aggregation system. Unfortunately, such systems have thousands of agents and have to consider demand uncertainty and the underlying problem is a (Partially Observable) Stochastic Game. Given the significant complexity of learning or planning in a stochastic game, we make three key contributions: (a) To exploit infinitesimally small contribution of each agent and anonymity (reward and transitions between agents are dependent on agent counts) in interactions, we represent this as a Multi-Agent Reinforcement Learning (MARL) problem that builds on insights from non-atomic congestion games model; (b) We provide a novel variance reduction mechanism for moving joint solution towards Nash Equilibrium that exploits the infinitesimally small contribution of each agent; and finally (c) We provide detailed results on three different domains to demonstrate the utility of our approach in comparison to state-of-the-art methods.
rate research
Read More
Strong empirical evidence that one machine-learning algorithm A outperforms another one B ideally calls for multiple trials optimizing the learning pipeline over sources of variation such as data sampling, data augmentation, parameter initialization, and hyperparameters choices. This is prohibitively expensive, and corners are cut to reach conclusions. We model the whole benchmarking process, revealing that variance due to data sampling, parameter initialization and hyperparameter choice impact markedly the results. We analyze the predominant comparison methods used today in the light of this variance. We show a counter-intuitive result that adding more sources of variation to an imperfect estimator approaches better the ideal estimator at a 51 times reduction in compute cost. Building on these results, we study the error rate of detecting improvements, on five different deep-learning tasks/architectures. This study leads us to propose recommendations for performance comparisons.
In the dictionary learning (or sparse coding) problem, we are given a collection of signals (vectors in $mathbb{R}^d$), and the goal is to find a basis in which the signals have a sparse (approximate) representation. The problem has received a lot of attention in signal processing, learning, and theoretical computer science. The problem is formalized as factorizing a matrix $X (d times n)$ (whose columns are the signals) as $X = AY$, where $A$ has a prescribed number $m$ of columns (typically $m ll n$), and $Y$ has columns that are $k$-sparse (typically $k ll d$). Most of the known theoretical results involve assuming that the columns of the unknown $A$ have certain incoherence properties, and that the coefficient matrix $Y$ has random (or partly random) structure. The goal of our work is to understand what can be said in the absence of such assumptions. Can we still find $A$ and $Y$ such that $X approx AY$? We show that this is possible, if we allow violating the bounds on $m$ and $k$ by appropriate factors that depend on $k$ and the desired approximation. Our results rely on an algorithm for what we call the threshold correlation problem, which turns out to be related to hypercontractive norms of matrices. We also show that our algorithmic ideas apply to a setting in which some of the columns of $X$ are outliers, thus giving similar guarantees even in this challenging setting.
Recent advances in deep reinforcement learning have achieved human-level performance on a variety of real-world applications. However, the current algorithms still suffer from poor gradient estimation with excessive variance, resulting in unstable training and poor sample efficiency. In our paper, we proposed an innovative optimization strategy by utilizing stochastic variance reduced gradient (SVRG) techniques. With extensive experiments on Atari domain, our method outperforms the deep q-learning baselines on 18 out of 20 games.
Existing few-shot learning (FSL) methods assume that there exist sufficient training samples from source classes for knowledge transfer to target classes with few training samples. However, this assumption is often invalid, especially when it comes to fine-grained recognition. In this work, we define a new FSL setting termed few-shot fewshot learning (FSFSL), under which both the source and target classes have limited training samples. To overcome the source class data scarcity problem, a natural option is to crawl images from the web with class names as search keywords. However, the crawled images are inevitably corrupted by large amount of noise (irrelevant images) and thus may harm the performance. To address this problem, we propose a graph convolutional network (GCN)-based label denoising (LDN) method to remove the irrelevant images. Further, with the cleaned web images as well as the original clean training images, we propose a GCN-based FSL method. For both the LDN and FSL tasks, a novel adaptive aggregation GCN (AdarGCN) model is proposed, which differs from existing GCN models in that adaptive aggregation is performed based on a multi-head multi-level aggregation module. With AdarGCN, how much and how far information carried by each graph node is propagated in the graph structure can be determined automatically, therefore alleviating the effects of both noisy and outlying training samples. Extensive experiments show the superior performance of our AdarGCN under both the new FSFSL and the conventional FSL settings.
In this paper we study the approximate minimization problem for language modelling. We assume we are given some language model as a black box. The objective is to obtain a weighted finite automaton (WFA) that fits within a given size constraint and which mimics the behaviour of the original model while minimizing some notion of distance between the black box and the extracted WFA. We provide an algorithm for the approximate minimization of black boxes trained for language modelling of sequential data over a one-letter alphabet. By reformulating the problem in terms of Hankel matrices, we leverage classical results on the approximation of Hankel operators, namely the celebrated Adamyan-Arov-Krein (AAK) theory. This allows us to use the spectral norm to measure the distance between the black box and the WFA. We provide theoretical guarantees to study the potentially infinite-rank Hankel matrix of the black box, without accessing the training data, and we prove that our method returns an asymptotically-optimal approximation.
suggested questions
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
