317 research outputs found
Methods of Nondifferentiable and Stochastic Optimization and Their Applications
Optimization methods are of a great practical importance in systems analysis. They allow us to find the best behavior of a system, determine the optimal structure and compute the optimal parameters of the control system etc. The development of nondifferentiable optimization, differentiable and nondifferentiable stochastic optimization allows us to state and effectively solve new complex optimization problems which were impossible to solve by classical optimization methods.
The main purpose of this article is to review briefly some important applications of nondifferentiable and stochastic optimization and to characterize principal directions of research. Clearly, the interests of the author have influenced the content of this article
Melding the Data-Decisions Pipeline: Decision-Focused Learning for Combinatorial Optimization
Creating impact in real-world settings requires artificial intelligence
techniques to span the full pipeline from data, to predictive models, to
decisions. These components are typically approached separately: a machine
learning model is first trained via a measure of predictive accuracy, and then
its predictions are used as input into an optimization algorithm which produces
a decision. However, the loss function used to train the model may easily be
misaligned with the end goal, which is to make the best decisions possible.
Hand-tuning the loss function to align with optimization is a difficult and
error-prone process (which is often skipped entirely).
We focus on combinatorial optimization problems and introduce a general
framework for decision-focused learning, where the machine learning model is
directly trained in conjunction with the optimization algorithm to produce
high-quality decisions. Technically, our contribution is a means of integrating
common classes of discrete optimization problems into deep learning or other
predictive models, which are typically trained via gradient descent. The main
idea is to use a continuous relaxation of the discrete problem to propagate
gradients through the optimization procedure. We instantiate this framework for
two broad classes of combinatorial problems: linear programs and submodular
maximization. Experimental results across a variety of domains show that
decision-focused learning often leads to improved optimization performance
compared to traditional methods. We find that standard measures of accuracy are
not a reliable proxy for a predictive model's utility in optimization, and our
method's ability to specify the true goal as the model's training objective
yields substantial dividends across a range of decision problems.Comment: Full version of paper accepted at AAAI 201
Supermodular mechanism design
This paper introduces a mechanism design approach that allows dealing with the multiple equilibrium problem, using mechanisms that are robust to bounded rationality. This approach is a tool for constructing supermodular mechanisms, i.e. mechanisms that induce games with strategic complementarities. In quasilinear environments, I prove that if a social choice function can be implemented by a mechanism that generates bounded strategic substitutes - as opposed to strategic complementarities - then this mechanism can be converted into a supermodular mechanism that implements the social choice function. If the social choice function also satisfies some efficiency criterion, then it admits a supermodular mechanism that balances the budget. Building on these results, I address the multiple equilibrium problem. I provide sufficient conditions for a social choice function to be implementable with a supermodular mechanism whose equilibria are contained in the smallest interval among all supermodular mechanisms. This is followed by conditions for supermodular implementability in unique equilibrium. Finally, I provide a revelation principle for supermodular implementation in environments with general preferences.Implementation, mechanisms, learning, strategic complementarities, supermodular games
System and Decision Sciences at IIASA 1973-1980
This report contains a brief history of the past achievements of the System and Decision Sciences Area at IIASA, and a summary of its current and future research directions. There is a comprehensive list of the scientific staff of the Area since 1973, together with a list of their publications; abstracts of the most recent reports and biographies of the scholars working in the Area in 1980 are also included
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