3 years ago

The value of randomized strategies in distributionally robust risk averse network interdiction games. (arXiv:2003.07915v1 [cs.GT])

Utsav Sadana, Erick Delage
Conditional Value at Risk (CVaR) is widely used to account for the preferences of a risk-averse agent in the extreme loss scenarios. To study the effectiveness of randomization in interdiction games with an interdictor that is both risk and ambiguity averse, we introduce a distributionally robust network interdiction game where the interdictor randomizes over the feasible interdiction plans in order to minimize the worst-case CVaR of the flow with respect to both the unknown distribution of the capacity of the arcs and his mixed strategy over interdicted arcs. The flow player, on the contrary, maximizes the total flow in the network. By using the budgeted uncertainty set, we control the degree of conservatism in the model and reformulate the interdictor's non-linear problem as a bi-convex optimization problem. For solving this problem to any given optimality level, we devise a spatial branch and bound algorithm that uses the McCormick inequalities and reduced reformulation linearization technique (RRLT) to obtain convex relaxation of the problem. We also develop a column generation algorithm to identify the optimal support of the convex relaxation which is then used in the coordinate descent algorithm to determine the upper bounds. The efficiency and convergence of the spatial branch and bound algorithm is established in the numerical experiments. Further, our numerical experiments show that randomized strategies can have significantly better in-sample and out-of-sample performance than optimal deterministic ones.

Publisher URL: http://arxiv.org/abs/2003.07915

DOI: arXiv:2003.07915v1

You might also like
Discover & Discuss Important Research

Keeping up-to-date with research can feel impossible, with papers being published faster than you'll ever be able to read them. That's where Researcher comes in: we're simplifying discovery and making important discussions happen. With over 19,000 sources, including peer-reviewed journals, preprints, blogs, universities, podcasts and Live events across 10 research areas, you'll never miss what's important to you. It's like social media, but better. Oh, and we should mention - it's free.

  • Download from Google Play
  • Download from App Store
  • Download from AppInChina

Researcher displays publicly available abstracts and doesn’t host any full article content. If the content is open access, we will direct clicks from the abstracts to the publisher website and display the PDF copy on our platform. Clicks to view the full text will be directed to the publisher website, where only users with subscriptions or access through their institution are able to view the full article.