Approximate Uncertain Programs

Uncertain programs are optimization problems involving uncertainties in constraints or objectives. In the past few decades, such programs have been applied in areas from economics and management to automotive control and machine learning. Because these problems are known to be NP-hard, many researchers have pursued approximate approaches, one of which – the scenario approach – replaces chance deterministic constraints with independent samples of uncertain parameters. This approach still faces serious challenges, however, as it offers no guarantee that an obtained solution is really optimal given prevailing probabilities. The solution found depends very strongly on the chosen samples.
As LML External Fellow Jiancang Zhuang and colleagues note in a new paper, several other approaches have been proposed to overcome this issue, including a Bayesian optimization framework which follows a data-driven approach for approximating an optimizer. This achieves solutions with a known probability of respecting the constraints. In their paper, the researchers aim to extend this work by using a single-layer feed forward neural network to approximate the uncertain constraints.
They demonstrate the new method through numerical simulations, comparing it with the standard scenario approach. Their results indicate that the proposed method is more robust in both finding an optimal solution and satisfying probability bounds on the violation of constraints. They also suggest that method can be further improved to converge in fewer iterations. This method may be useful in various industrial areas, including energy management for hybrid vehicles, decision making models for autonomous vehicles and decision strategy within electricity markets.
The paper is available at

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