Online distributed optimization with stochastic gradients:high probability bound of regrets

In this paper,the problem of online distributed optimization subject to a convex set is studied via a network of agents.Each agent only has access to a noisy gradient of its own objective function,and can communicate with its neighbors via a network.To handle this problem,an online distributed stochastic mirror descent algorithm is proposed.Existing works on online distributed algorithms involving stochastic gradients only provide the expectation bounds of the regrets.Different from them,we study the high probability bound of the regrets,i.e.,the sublinear bound of the regret is characterized by the natural logarithm of the failure probability's inverse.Under mild assumptions on the graph connectivity,we prove that the dynamic regret grows sublinearly with a high probability if the deviation in the minimizer sequence is sublinear with the square root of the time horizon.Finally,a simulation is provided to demonstrate the effectiveness of our theoretical results.

The ocean response to climate change guides both adaptation and mitigation efforts

The ocean’s thermal inertia is a major contributor to irreversible ocean changes exceeding time scales that matter to human society.This fact is a challenge to societies as they prepare for the consequences of climate change,especially with respect to the ocean.Here the authors review the requirements for human actions from the ocean’s perspective.In the near term(∼2030),goals such as the United Nations Sustainable Development Goals(SDGs)will be critical.Over longer times(∼2050–2060 and beyond),global carbon neutrality targets may be met as countries continue to work toward reducing emissions.Both adaptation and mitigation plans need to be fully implemented in the interim,and the Global Ocean Observation System should be sustained so that changes can be continuously monitored.In the longer-term(after∼2060),slow emerging changes such as deep ocean warming and sea level rise are committed to continue even in the scenario where net zero emissions are reached.Thus,climate actions have to extend to time scales of hundreds of years.At these time scales,preparation for“high impact,low probability”risks—such as an abrupt showdown of Atlantic Meridional Overturning Circulation,ecosystem change,or irreversible ice sheet loss—should be fully integrated into long-term planning.

A Symmetric Linearized Alternating Direction Method of Multipliers for a Class of Stochastic Optimization Problems

Alternating direction method of multipliers(ADMM)receives much attention in the recent years due to various demands from machine learning and big data related optimization.In 2013,Ouyang et al.extend the ADMM to the stochastic setting for solving some stochastic optimization problems,inspired by the structural risk minimization principle.In this paper,we consider a stochastic variant of symmetric ADMM,named symmetric stochastic linearized ADMM(SSL-ADMM).In particular,using the framework of variational inequality,we analyze the convergence properties of SSL-ADMM.Moreover,we show that,with high probability,SSL-ADMM has O((ln N)·N^(-1/2))constraint violation bound and objective error bound for convex problems,and has O((ln N)^(2)·N^(-1))constraint violation bound and objective error bound for strongly convex problems,where N is the iteration number.Symmetric ADMM can improve the algorithmic performance compared to classical ADMM,numerical experiments for statistical machine learning show that such an improvement is also present in the stochastic setting.