25 research outputs found
Variational inference formulation for a model-free simulation of a dynamical system with unknown parameters by a recurrent neural network
We propose a recurrent neural network for a "model-free" simulation of a
dynamical system with unknown parameters without prior knowledge. The deep
learning model aims to jointly learn the nonlinear time marching operator and
the effects of the unknown parameters from a time series dataset. We assume
that the time series data set consists of an ensemble of trajectories for a
range of the parameters. The learning task is formulated as a statistical
inference problem by considering the unknown parameters as random variables. A
latent variable is introduced to model the effects of the unknown parameters,
and a variational inference method is employed to simultaneously train
probabilistic models for the time marching operator and an approximate
posterior distribution for the latent variable. Unlike the classical
variational inference, where a factorized distribution is used to approximate
the posterior, we employ a feedforward neural network supplemented by an
encoder recurrent neural network to develop a more flexible probabilistic
model. The approximate posterior distribution makes an inference on a
trajectory to identify the effects of the unknown parameters. The time marching
operator is approximated by a recurrent neural network, which takes a latent
state sampled from the approximate posterior distribution as one of the input
variables, to compute the time evolution of the probability distribution
conditioned on the latent variable. In the numerical experiments, it is shown
that the proposed variational inference model makes a more accurate simulation
compared to the standard recurrent neural networks. It is found that the
proposed deep learning model is capable of correctly identifying the dimensions
of the random parameters and learning a representation of complex time series
data
Finite-Sum Smooth Optimization with SARAH
The total complexity (measured as the total number of gradient computations)
of a stochastic first-order optimization algorithm that finds a first-order
stationary point of a finite-sum smooth nonconvex objective function
has been proven to be at least
for where
denotes the attained accuracy for the outputted approximation
(Fang et al., 2018). In this paper, we provide a convergence analysis for a
slightly modified version of the SARAH algorithm (Nguyen et al., 2017a;b) and
achieve total complexity that matches the lower-bound worst case complexity in
(Fang et al., 2018) up to a constant factor when for nonconvex problems. For convex optimization, we
propose SARAH++ with sublinear convergence for general convex and linear
convergence for strongly convex problems; and we provide a practical version
for which numerical experiments on various datasets show an improved
performance
Finite-Sum Smooth Optimization with SARAH
The total complexity (measured as the total number of gradient computations) of a stochastic first-order optimization algorithm that finds a first-order stationary point of a finite-sum smooth nonconvex objective function F(w)=1n∑ni=1fi(w) has been proven to be at least Ω(n−−√/ϵ) for n≤O(ϵ−2) where ϵ denotes the attained accuracy E[∥∇F(w~)∥2]≤ϵ for the outputted approximation w~ (Fang et al., 2018). In this paper, we provide a convergence analysis for a slightly modified version of the SARAH algorithm (Nguyen et al., 2017a;b) and achieve total complexity that matches the lower-bound worst case complexity in (Fang et al., 2018) up to a constant factor when n≤O(ϵ−2) for nonconvex problems. For convex optimization, we propose SARAH++ with sublinear convergence for general convex and linear convergence for strongly convex problems; and we provide a practical version for which numerical experiments on various datasets show an improved performance
Winner Determination in MultiAttribute Auctions
In view of the transfer of copyright to the outside publisher, its distribution outside of IBM prior to publication should be limited to peer communications and specific requests. After outside publication, requests should be filled only by reprints or legally obtained copies of the article (e.g., payment of royalties). Copies may be requested from IBM T. J. Watson Research Center
Software Frameworks for Advanced Procurement Auction Markets
Abstract. Traditional auctions such as the English and first-price sealed-bid auctions have been adopted as another tool for procurement negotiations. Throughout the past decade many new auction formats have been developed, which support more general negotiation situations relevant to industrial sourcing and procurement. A number of software solutions have been developed for this emerging market. Designing respective auction frameworks requires consideration of economic and computational aspects. This paper discusses a respective framework relevant to the design of software platforms for advanced procurement auction markets
RECO: Representation and Evaluation of Configurable Offers
Abstract: Up until now, electronic negotiations have primarily focused on the trading of simple goods and services, where products can be described either by price alone or as a set of attributes. There is little support for trading complex, configurable products, such as computer systems, automobiles, insurances and services in general. Companies need to communicate offers including complex rules and business policies, and they need decision support to evaluate these offers. This paper describes RECO, a decision support system for the representation and evaluation of configurable offers. Configurable offers allow multiple values for each attribute and they include rules on how to combine the various attribute values and how to price a desired configuration. From a configurable offer, a user can extract offers for individual configurations. RECO provides a compact representation for configurable offers using prepositional logic, and helps a user in finding the top L configurations based on her preferences. In a multi-sourcing setting, it provides support for identifying the optimal sourcing strategy subject to considerations such as minimum/maximium number of winners and homogeneity of attributes across bids. We draw on mathematical programming, propositional logic and decision analysis
Cooperative Strategies for Solving the Bicriteria Sparse Multiple Knapsack Problem
For hard optimization problems, it is difficult to design heuristic algorithms which exhibit uniformly superior performance for all problem instances. As a result it becomes necessary to tailor the algorithms based on the problem instance. In this paper, we introduce the use of a cooperative problem solving team of heuristics that evolves algorithms for a given problem instance. The efficacy of this method is examined by solving six difficult instances of a bicriteria sparse multiple knapsack problem. Results indicate that such tailored algorithms uniformly improve solutions as compared to using predesigned heuristic algorithms