# Multi-Objective Learning over Adaptive Networks

**Speaker:** Chung-Kai Yu
**Affiliation:** Ph.D. Candidate - UCLA

**Abstract:** This dissertation deals with the design of learning strategies over adaptive networks under several constraint scenarios such as (a) having agents with different but complementary objectives; (b) having agents with access to only partial information; and (c) having selfish agents that seek to reduce their own communication cost at the expense of the social good for the overall network.

Adaptive networks consist of collections of agents with learning abilities that interact with each other locally in order to solve distributed processing and inference tasks in real-time. In our first constrained problem, we examine the design and evolution of adaptive networks in which agents have multiple and distinct objectives and, consequently, selfish learning strategies by individual agents can influence the network dynamics in adverse ways. This situation is even more challenging in nonstationary environments where the solution to the multi-objective optimization problem can drift with time due to changes in the statistical distribution of the data.

We consider a general formulation of multi-objective optimization problems over network topologies where agents seek to minimize their individual costs subject to constraints that are locally coupled. The coupling arises because the individual costs and the constraints can be dependent on actions by other agents in the neighborhood. In these types of problems, the Nash equilibrium is a desired and stable solution since at this location no agent can benefit by unilaterally deviating from the equilibrium. We therefore focus on developing distributed online strategies that enable agents to approach the Nash equilibrium. We illustrate an application of the results to a stochastic version of the network Cournot competition problem, which arises in a variety of useful problems such as in modeling economic trading with geographical considerations, power management over smart grids, and resource allocation protocols.

Using this formulation, we then extend earlier contributions on adaptive networks, which generally assume that the agents work together for a common global objective or when they observe data that is generated by a common target model or parameter vector. We relax this condition and consider a broader scenario where individual agents may only have access to partial information about the global target vector, i.e., each agent may be sensing only a subset of the entries of the global target, and the number of these entries can be different across the agents. We develop cooperative distributed techniques where agents are only required to share estimates of their common entries and still can benefit from neighboring agents. Since agents’ interactions are limited to exchanging estimates of select few entries, communication overhead is significantly reduced.

**Biography:**** **Chung-Kai Yu is currently a Ph.D. candidate in the Electrical Engineering Department at the University of California, Los Angeles (UCLA). He received the B.S. and M.S. degrees in Electrical Engineering from National Taiwan University (NTU), in 2006 and 2008, respectively. From 2008 to 2011, he was a research assistant in the Wireless Broadband Communication System Laboratory at NTU. Chung-Kai received the UCLA dissertation year fellowship in 2016-2017. His research interests include game-theoretic learning, adaptive networks, and distributed optimization.

*For more information, contact Prof. Ali H. Sayed () *** **

**Date/Time:**

Date(s) - Mar 01, 2017*9:30 am - 12:30 pm*

**Location:**

E-IV Tesla Room #53-125

420 Westwood Plaza - 5th Flr., Los Angeles CA 90095