Doing-it-All with Bounded Work and Communication

We consider the Do-All problem, where $p$ cooperating processors need to complete $t$ similar and independent tasks in an adversarial setting. Here we deal with a synchronous message passing system with processors that are subject to crash failures. Efficiency of algorithms in this setting is measured in terms of work complexity (also known as total available processor steps) and communication complexity (total number of point-to-point messages). When work and communication are considered to be comparable resources, then the overall efficiency is meaningfully expressed in terms of effort defined as work + communication. We develop and analyze a constructive algorithm that has work $O( t + p \log p\, (\sqrt{p\log p}+\sqrt{t\log t}\, ) )$ and a nonconstructive algorithm that has work $O(t +p \log^2 p)$. The latter result is close to the lower bound $\Omega(t + p \log p/ \log \log p)$ on work. The effort of each of these algorithms is proportional to its work when the number of crashes is bounded above by $c\,p$, for some positive constant $c < 1$. We also present a nonconstructive algorithm that has effort $O(t + p ^{1.77})$

Pure Exploration with Multiple Correct Answers

We determine the sample complexity of pure exploration bandit problems with multiple good answers. We derive a lower bound using a new game equilibrium argument. We show how continuity and convexity properties of single-answer problems ensures that the Track-and-Stop algorithm has asymptotically optimal sample complexity. However, that convexity is lost when going to the multiple-answer setting. We present a new algorithm which extends Track-and-Stop to the multiple-answer case and has asymptotic sample complexity matching the lower bound

Software tools for stochastic programming: A Stochastic Programming Integrated Environment (SPInE)

SP models combine the paradigm of dynamic linear programming with modelling of random parameters, providing optimal decisions which hedge against future uncertainties. Advances in hardware as well as software techniques and solution methods have made SP a viable optimisation tool. We identify a growing need for modelling systems which support the creation and investigation of SP problems. Our SPInE system integrates a number of components which include a flexible modelling tool (based on stochastic extensions of the algebraic modelling languages AMPL and MPL), stochastic solvers, as well as special purpose scenario generators and database tools. We introduce an asset/liability management model and illustrate how SPInE can be used to create and process this model as a multistage SP application

SNAP: Stateful Network-Wide Abstractions for Packet Processing

Early programming languages for software-defined networking (SDN) were built on top of the simple match-action paradigm offered by OpenFlow 1.0. However, emerging hardware and software switches offer much more sophisticated support for persistent state in the data plane, without involving a central controller. Nevertheless, managing stateful, distributed systems efficiently and correctly is known to be one of the most challenging programming problems. To simplify this new SDN problem, we introduce SNAP. SNAP offers a simpler "centralized" stateful programming model, by allowing programmers to develop programs on top of one big switch rather than many. These programs may contain reads and writes to global, persistent arrays, and as a result, programmers can implement a broad range of applications, from stateful firewalls to fine-grained traffic monitoring. The SNAP compiler relieves programmers of having to worry about how to distribute, place, and optimize access to these stateful arrays by doing it all for them. More specifically, the compiler discovers read/write dependencies between arrays and translates one-big-switch programs into an efficient internal representation based on a novel variant of binary decision diagrams. This internal representation is used to construct a mixed-integer linear program, which jointly optimizes the placement of state and the routing of traffic across the underlying physical topology. We have implemented a prototype compiler and applied it to about 20 SNAP programs over various topologies to demonstrate our techniques' scalability

Conic Optimization Theory: Convexification Techniques and Numerical Algorithms

Optimization is at the core of control theory and appears in several areas of this field, such as optimal control, distributed control, system identification, robust control, state estimation, model predictive control and dynamic programming. The recent advances in various topics of modern optimization have also been revamping the area of machine learning. Motivated by the crucial role of optimization theory in the design, analysis, control and operation of real-world systems, this tutorial paper offers a detailed overview of some major advances in this area, namely conic optimization and its emerging applications. First, we discuss the importance of conic optimization in different areas. Then, we explain seminal results on the design of hierarchies of convex relaxations for a wide range of nonconvex problems. Finally, we study different numerical algorithms for large-scale conic optimization problems.Comment: 18 page