Exponentially Fast Parameter Estimation in Networks Using Distributed Dual Averaging

In this paper we present an optimization-based view of distributed parameter estimation and observational social learning in networks. Agents receive a sequence of random, independent and identically distributed (i.i.d.) signals, each of which individually may not be informative about the underlying true state, but the signals together are globally informative enough to make the true state identifiable. Using an optimization-based characterization of Bayesian learning as proximal stochastic gradient descent (with Kullback-Leibler divergence from a prior as a proximal function), we show how to efficiently use a distributed, online variant of Nesterov's dual averaging method to solve the estimation with purely local information. When the true state is globally identifiable, and the network is connected, we prove that agents eventually learn the true parameter using a randomized gossip scheme. We demonstrate that with high probability the convergence is exponentially fast with a rate dependent on the KL divergence of observations under the true state from observations under the second likeliest state. Furthermore, our work also highlights the possibility of learning under continuous adaptation of network which is a consequence of employing constant, unit stepsize for the algorithm.Comment: 6 pages, To appear in Conference on Decision and Control 201

Online Learning with Gaussian Payoffs and Side Observations

We consider a sequential learning problem with Gaussian payoffs and side information: after selecting an action $i$, the learner receives information about the payoff of every action $j$ in the form of Gaussian observations whose mean is the same as the mean payoff, but the variance depends on the pair $(i,j)$ (and may be infinite). The setup allows a more refined information transfer from one action to another than previous partial monitoring setups, including the recently introduced graph-structured feedback case. For the first time in the literature, we provide non-asymptotic problem-dependent lower bounds on the regret of any algorithm, which recover existing asymptotic problem-dependent lower bounds and finite-time minimax lower bounds available in the literature. We also provide algorithms that achieve the problem-dependent lower bound (up to some universal constant factor) or the minimax lower bounds (up to logarithmic factors)

The emerging role of inventory management in small restaurants: Developing an effective inventory management system for a small pizza shop

The inventory management system is foremost in each association; particularly such associations who supply goods in advance for trade to consumers. This study project is determined on the place of work of the researcher, “Poppas Pizza.” The study is limited to learning the inventory management system of “Poppas Pizza”, classifying the limitations of the inventory system of the shop, and recommending solutions to progress the inventory management system of the shop. The entire research is dependent on the qualitative technique involving the personal observations of the researcher and, furthermore, with carrying out discussions with the shop director to identify information about these weaknesses. The study found weaknesses of the shop through learning the present inventory management system of the shop, and suggestions has been completed to progress the technique. The suggestions were completed through the previous studies and from the interviews

Sequential Gaussian Processes for Online Learning of Nonstationary Functions

Many machine learning problems can be framed in the context of estimating functions, and often these are time-dependent functions that are estimated in real-time as observations arrive. Gaussian processes (GPs) are an attractive choice for modeling real-valued nonlinear functions due to their flexibility and uncertainty quantification. However, the typical GP regression model suffers from several drawbacks: i) Conventional GP inference scales $O(N^{3})$ with respect to the number of observations; ii) updating a GP model sequentially is not trivial; and iii) covariance kernels often enforce stationarity constraints on the function, while GPs with non-stationary covariance kernels are often intractable to use in practice. To overcome these issues, we propose an online sequential Monte Carlo algorithm to fit mixtures of GPs that capture non-stationary behavior while allowing for fast, distributed inference. By formulating hyperparameter optimization as a multi-armed bandit problem, we accelerate mixing for real time inference. Our approach empirically improves performance over state-of-the-art methods for online GP estimation in the context of prediction for simulated non-stationary data and hospital time series data