We analyze stochastic gradient algorithms for optimizing nonconvex, nonsmooth finite-sum problems. In particular, the objective function is given by the summation of a differentiable (possibly nonconvex) component, together with a possibly non-differentiable but convex component. We propose a proximal stochastic gradient algorithm based on variance reduction, called ProxSVRG+. Our main contribution lies in the analysis of ProxSVRG+. It recovers several existing convergence results and improves/generalizes them (in terms of the number of stochastic gradient oracle calls and proximal oracle calls). In particular, ProxSVRG+ generalizes the best results given by the SCSG algorithm, recently proposed by [Lei et al., NIPS'17] for the smooth nonconvex case. ProxSVRG+ is also more straightforward than SCSG and yields simpler analysis. Moreover, ProxSVRG+ outperforms the deterministic proximal gradient descent (ProxGD) for a wide range of minibatch sizes, which partially solves an open problem proposed in [Reddi et al., NIPS'16].

Iraq's Prime Minister Mohammed Shia al-Sudani faces pressure to act against Iran-backed terrorist groups following increased attacks on U.S., European, and Kurdish assets in the country.

They don't cope well in certain situations and the'transparent' mode lets in unwanted noise

President Donald Trump warns NATO allies they face a 'very bad' future if they don't help defend the Strait of Hormuz, telling The Financial Times beneficiaries should assist.

Timothee Chalamet, Oscars laughing stock: All the brutal digs aimed at star after he missed out on Best Actor and'looked like he wanted to cry' A-list stars ditch formal Oscars red carpet dresses for sexy party looks - with Jeff Goldblum's wife Emilie Livingston, Heidi Klum, Amelia Gray Hamlin and Kate Hudson turning up the heat at Vanity Fair bash Teyana Taylor erupts backstage at Oscars after being'shoved' Chilling new details of dismembered Emily Pike's final hours after she was snatched in Arizona desert and man detectives now believe murdered her Dark truth about secret new filler treatment that uses tissue from DEAD PEOPLE... as doctors issue urgent warning Awful Timothee Chalamet's ego is bigger than Kylie's inflated butt... but it's so clear what's really going on here. Israel blows up Ayatollah Khamenei's personal jet amid claims his injured heir Mojtaba'has been flown to Moscow for treatment' Kate lets Diana take the spotlight: Princess skips Mother's Day post after emotional cancer message and Photoshop furore Baseball fans fume after'terrible' umpire error ends USA's controversial showdown with Dominican Republic in WBC semifinal How Oscars 2026 proved Hollywood has overdosed on Ozempic: Leading doctors name stars now at'extreme' risk... and reveal terrifying new side effects Trump warns of'very bad future' for Nato if his call for warships to police Strait of Hormuz is refused - hinting he could punish Ukraine Kim Kardashian struggles to WALK in skintight golden gown and towering'stripper heels' as she attends the Vanity Fair Oscars party Oscars presenter Kumail Nanjiani blasted for horrific Holocaust joke: 'Do not invite him back' Real reason Sean Penn skipped Oscars 2026... as disappointed fans blast his boycott'It's like he was possessed': Terrifying moment Alexander brother turned into a'monster' and raped me... and the four chilling words he said after horror attack - alleged victim claims Dubai'arrests foreign survivors of Iranian drone strike after they sent images of explosion aftermath to loved ones to prove they were safe' The Mediterranean is overdue a TSUNAMI: Scientists warn there's a 100% chance an enormous wave will hit the French Riviera in the next 30 years - as they call for urgent evacuation drills The French Riviera is famed for its sunny, year-round climate, azure waters and luxury resorts - but it'll be hit by a tsunami in the next 30 years, scientists predict. Experts say there is a '100 per cent' chance a great wave will form in the Mediterranean Sea in the next few decades. The tsunami could hit France's southern coastline in as little as 10 minutes from the trigger, causing chaos for tens of thousands of people who flock there during the summer months. While the country does have a national tsunami alert system, this only covers waves caused by distant earthquakes .

Variational inference is increasingly being addressed with stochastic optimization. In this setting, the gradient's variance plays a crucial role in the optimization procedure, since high variance gradients lead to poor convergence. A popular approach used to reduce gradient's variance involves the use of control variates. Despite the good results obtained, control variates developed for variational inference are typically looked at in isolation. In this paper we clarify the large number of control variates that are available by giving a systematic view of how they are derived. We also present a Bayesian risk minimization framework in which the quality of a procedure for combining control variates is quantified by its effect on optimization convergence rates, which leads to a very simple combination rule. Results show that combining a large number of control variates this way significantly improves the convergence of inference over using the typical gradient estimators or a reduced number of control variates.

Timothee Chalamet, Oscars laughing stock: All the brutal digs aimed at star after he missed out on Best Actor and'looked like he wanted to cry' A-list stars ditch formal Oscars red carpet dresses for sexy party looks - with Jeff Goldblum's wife Emilie Livingston, Heidi Klum, Amelia Gray Hamlin and Kate Hudson turning up the heat at Vanity Fair bash Teyana Taylor erupts backstage at Oscars after being'shoved' Chilling new details of dismembered Emily Pike's final hours after she was snatched in Arizona desert and man detectives now believe murdered her Dark truth about secret new filler treatment that uses tissue from DEAD PEOPLE... as doctors issue urgent warning Awful Timothee Chalamet's ego is bigger than Kylie's inflated butt... but it's so clear what's really going on here. Israel blows up Ayatollah Khamenei's personal jet amid claims his injured heir Mojtaba'has been flown to Moscow for treatment' Kate lets Diana take the spotlight: Princess skips Mother's Day post after emotional cancer message and Photoshop furore Baseball fans fume after'terrible' umpire error ends USA's controversial showdown with Dominican Republic in WBC semifinal How Oscars 2026 proved Hollywood has overdosed on Ozempic: Leading doctors name stars now at'extreme' risk... and reveal terrifying new side effects Trump warns of'very bad future' for Nato if his call for warships to police Strait of Hormuz is refused - hinting he could punish Ukraine Kim Kardashian struggles to WALK in skintight golden gown and towering'stripper heels' as she attends the Vanity Fair Oscars party Oscars presenter Kumail Nanjiani blasted for horrific Holocaust joke: 'Do not invite him back' Real reason Sean Penn skipped Oscars 2026... as disappointed fans blast his boycott'It's like he was possessed': Terrifying moment Alexander brother turned into a'monster' and raped me... and the four chilling words he said after horror attack - alleged victim claims Dubai'arrests foreign survivors of Iranian drone strike after they sent images of explosion aftermath to loved ones to prove they were safe' Is Antarctica's Doomsday Glacier about to COLLAPSE? Antarctica's Doomsday Glacier could'snowball' towards collapse, as a study shows the ice is melting faster than expected. Scientists from the University of Edinburgh predict that the glacier - whose official name is Thwaites - could shed 200 gigatonnes of ice every single year by 2067. That is more than the current ice loss of the entire Antarctic Ice Sheet, which has been losing 150 gigatonnes of ice per year for the last two decades.

The EV manufacturer is supported by a robust online community. But Elon Musk's politics and overblown hype about Full Self-Driving are turning some loyalists away. This month, Tesla customers erupted in outrage over what some called a " bait and switch " by the electric vehicle manufacturer. Initially, the company had offered to transfer the Full Self-Driving feature, which is now only available through a subscription model but could once be purchased for a "lifetime" fee that ran as high as $15,000, to any new Tesla purchased by March 31. The deal was most tempting for drivers already enticed by a new base Cybertruck model that cost just $59,990, a price that CEO Elon Musk soon clarified would only last for 10 days, leaving potential buyers a very small window to make up their minds. Then Tesla quietly amended the language of the FSD transfer agreement, stipulating that customers would need to take delivery of a Tesla by March 31 in order to swap their FSD from their last vehicle to the next.

What are the symptoms of meningitis and is there a vaccine? Two people have died following an outbreak of meningitis in Kent. The death of a year 13 pupil at Queen Elizabeth's Grammar School in Faversham was confirmed by the local MP on Monday. The second person who died was a student at the University of Kent. The UK Health Security Agency (UKHSA) said it was notified of 13 cases with signs and symptoms of meningitis and septicaemia from Friday to Sunday in the Canterbury area.

A bicycle wheel with guitar strings, a touch-operated synth, and the "Demon Box" were just a few of the new instruments on show at Georgia Tech's Guthman Musical Instrument Competition this weekend. An open-source, touch-operated synth built to resemble a puzzle piece and keep accessibility at the forefront. A pressure-sensitive surface allows for polyphonic synthesis that can be triggered by hands, feet, textured fabrics, or even Play-Doh. Brand new sounds floated through a concert hall at Georgia Tech this weekend, as the 28th annual Guthman Musical Instrument Competition showcased an array of new instruments from around the world--and crowned one champion. Ten finalists, chosen from candidates who built all kinds of new music-making devices, converged in Atlanta, Georgia, to present their instruments to a panel of judges.