Estimation of Learning Dynamics in the Routing Game. Online Learning and Optimization: We call such algorithms AREP approximate replicator algorithms, as they can be interpreted as a discrete-time approximation of the replicator equation, which models the continuous-time evolution of population strategies, and which is known to converge for the class of congestion games. This results in an optimal control problem under learning dynamics. From Continuous to Discrete Time. Our paper on accelerated mirror descent in continuous and discrete time is selected for a spotlight presentation at NIPS. In the Stackelberg routing game, a central authority leader is assumed to have control over a fraction of the flow on the network compliant flow , and the remaining flow responds selfishly.

We pose the following estimation problem: I also work on developing optimization methods using continuous-time and stochastic dynamics. Convergence in routing games and beyond. In this paper, we consider privacy in the routing game, where the origins and destinations of drivers are considered private. Classes are growing in size and adding more and more technology. We also use the estimated model parameters to predict the flow distribution over routes, and compare our predictions to the actual distributions, showing that the online learning model can be used as a predictive model over short horizons. These results provide a distributed learning model that is robust to measurement noise and other stochastic perturbations, and allows flexibility in the choice of learning algorithm of each player.

If the learning dynamics are heterogeneous, that is, different players use different learning rates, then the joint strategy converges to equilibrium in expectation, and we give upper bounds on the convergence rate. This connection between accelerated mirror descent and the ODE provides an intuitive approach to the design and analysis of accelerated first-order algorithms. I will give a talk on continuous-time optimization methods at the Machine Learning and Trends in Optimization seminar at the University of Washington, on February 20, In particular, we show how the asymptotic rate of covariation affects the choice of parameters and, ultimately, the convergence rate.

For this new class, some results from the classical congestion games literature in which latency is assumed to be a non-decreasing function of the flow do not hold.

## Kate Harrison

Acceleration and Averaging in Stochastic Descent Dynamics. We study the problem of learning similarity functions over very large corpora using neural network embedding models. Numerical simulations on the I15 freeway in California demonstrate an improvement in performance and running time compared with existing bwrkeley.

We propose different methods tapk approximately solving this problem: Then, by carefully discretizing the ODE, we obtain a family of accelerated algorithms with optimal rate of convergence.

We consider in particular a model in which players update their strategies using algorithms with sublinear discounted regret.

The echo train ordering is randomly shuffled during the acquisition according to variable density Poisson disk sampling masks. Krichene, and Itamar Rossen. The method mitigates image blur and rerospectively synthesizes T1-weighted and T2-weighted volumetric images.

Kristin Stephens-Martinez is a Ph. Then we study the Stackelberg routing game: The method accounts for temporal dynamics during the echo trains to reduce image blur and resolve multiple image contrasts along the T2 relaxation curve. At each iteration, we choose an action from X’, based on the observed sequence of previous rewards. Under the assumption of uniformly didsertation rewards, we obtain explicit regret bounds in a setting where the decision set is the set of probability distributions on a compact metric space S.

This work is applied to modeling and simulating congestion mitigation on transportation networks, in which a coordinator traffic fecs agency can choose to route a fraction of compliant drivers, while the rest of the drivers choose their routes selfishly.

Our goal is to minimize regret, defined as the gap between the realized reward and the reward of the best fixed action in hindsight. I like working with undergraduates on interesting projects.

# Jon Tamir – Home

In this thesis, we apply this paradigm to two problems: In the Stackelberg routing game, a central authority leader is assumed to have control over a fraction of the flow on the network compliant flowand the remaining flow responds selfishly.

We further give a more refined analysis of these dynamics and their convergence rates. We conduct large-scale experiments that show a significant improvement both in training time and generalization performance compared to sampling methods.

We adopt a flow dynamics model that is a Godunov discretization of the Lighthillâ€”Williamsâ€”Richards partial differential equation with a triangular flux function and a corresponding multicommodity junction solver. We analyze the berkrley of this process and provide theoretical guarantees on the convergence rates as well as differential privacy values for these models.

We show that it is optimal for this new class of latency on parallel networks. We define a multicommodity junction model that only requires full Lagrangian paths for the controllable agents, and aggregate turn ratios for the noncontrollable selfish agents. The method is disserrtation to the problem of coordinated ramp metering on freeway networks.

# BID – Berkeley Institute of Design

Eeds confirm these with simulations on a small example. We show that it can be guaranteed for a class of algorithms with a sublinear discounted regret and which satisfy an additional condition.

We then propose an adaptive averaging heuristic which adaptively computes the weights to speed up the decrease of the Lyapunov function. I will be giving a talk at the IPAM on distributed learning, estimation and control for routing November I am primarily interested in applying advanced imaging and reconstruction techniques to pediatric MRI, with the goal of enabling real clinical adoption. The game is stochastic in that each player observes a stochastic vector, the conditional expectation of which is equal to the true loss almost surely.