401,499 research outputs found
Online Network Design under Uncertainty
Today, computer and information networks play a significant role in the success of businesses, both large and small. Networks provide access to various services and resources to end users and devices. There has been extensive research on de- signing networks according to numerous criteria such as cost-efficiency, availability, adaptivity, survivability, among others. In this dissertation, we revisit some of the most fundamental network design problems in the presence of uncertainty.
In most realistic models, we are forced to make decisions in the presence of an incomplete input, which is the source of uncertainty for an optimization algorithm. There are different types of uncertainty. For example, in stochastic settings, we may have some random variables derived from some known/unknown distributions. In online settings, the complete input is not known in a-priori and pieces of the input become available sequentially; leaving the algorithm to make decisions only with partial data.
In this dissertation, we consider network design and network optimization problems with uncertainty. In particular, we study online bounded-degree Steiner network design, online survivable network design, and stochastic k-server. We analyze their complexity and design competitive algorithms for them
Learning Predictive Safety Filter via Decomposition of Robust Invariant Set
Ensuring safety of nonlinear systems under model uncertainty and external
disturbances is crucial, especially for real-world control tasks. Predictive
methods such as robust model predictive control (RMPC) require solving
nonconvex optimization problems online, which leads to high computational
burden and poor scalability. Reinforcement learning (RL) works well with
complex systems, but pays the price of losing rigorous safety guarantee. This
paper presents a theoretical framework that bridges the advantages of both RMPC
and RL to synthesize safety filters for nonlinear systems with state- and
action-dependent uncertainty. We decompose the robust invariant set (RIS) into
two parts: a target set that aligns with terminal region design of RMPC, and a
reach-avoid set that accounts for the rest of RIS. We propose a policy
iteration approach for robust reach-avoid problems and establish its monotone
convergence. This method sets the stage for an adversarial actor-critic deep RL
algorithm, which simultaneously synthesizes a reach-avoid policy network, a
disturbance policy network, and a reach-avoid value network. The learned
reach-avoid policy network is utilized to generate nominal trajectories for
online verification, which filters potentially unsafe actions that may drive
the system into unsafe regions when worst-case disturbances are applied. We
formulate a second-order cone programming (SOCP) approach for online
verification using system level synthesis, which optimizes for the worst-case
reach-avoid value of any possible trajectories. The proposed safety filter
requires much lower computational complexity than RMPC and still enjoys
persistent robust safety guarantee. The effectiveness of our method is
illustrated through a numerical example
Online Predictive Optimization Framework for Stochastic Demand-Responsive Transit Services
This study develops an online predictive optimization framework for
dynamically operating a transit service in an area of crowd movements. The
proposed framework integrates demand prediction and supply optimization to
periodically redesign the service routes based on recently observed demand. To
predict demand for the service, we use Quantile Regression to estimate the
marginal distribution of movement counts between each pair of serviced
locations. The framework then combines these marginals into a joint demand
distribution by constructing a Gaussian copula, which captures the structure of
correlation between the marginals. For supply optimization, we devise a linear
programming model, which simultaneously determines the route structure and the
service frequency according to the predicted demand. Importantly, our framework
both preserves the uncertainty structure of future demand and leverages this
for robust route optimization, while keeping both components decoupled. We
evaluate our framework using a real-world case study of autonomous mobility in
a university campus in Denmark. The results show that our framework often
obtains the ground truth optimal solution, and can outperform conventional
methods for route optimization, which do not leverage full predictive
distributions.Comment: 34 pages, 12 figures, 5 table
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