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Recently there is a large amount of work devoted to the study of Markov chain stochastic gradient methods (MC-SGMs) which mainly focus on their convergence analysis for solving minimization problems. In this paper, we provide a comprehensive generalization analysis of MC-SGMs for both minimization and minimax problems through the lens of algorithmic stability in the framework of statistical learning theory. For empirical risk minimization (ERM) problems, we establish the optimal excess population risk bounds for both smooth and non-smooth cases by introducing on-average argument stability. For minimax problems, we develop a quantitative connection between on-average argument stability and generalization error which extends the existing results for uniform stability [38]. We further develop the first nearly optimal convergence rates for convex-concave problems both in expectation and with high probability, which, combined with our stability results, show that the optimal generalization bounds can be attained for both smooth and non-smooth cases. To the best of our knowledge, this is the first generalization analysis of SGMs when the gradients are sampled from a Markov process.

Valve's £85 Steam Controller divides gamers ahead of May launch Valve has announced its new Steam Controller will be available to order from 4 May, and will cost £85 in the UK and $99 in the US - prices that have raised eyebrows among some gamers. The second generation of the gamepad, it will be compatible with PCs and Valve's handheld console, the Steam Deck. It is also designed to work with the company's own upcoming gaming PC, the Steam Machine. The Steam Controller may be more expensive than the standard controllers from Nintendo, Xbox and PlayStation, but we do live in a time where companies including Sony and Microsoft are selling premium controllers for £150-£200, said Chris Scullion deputy editor of Video Games Chronicle. There has been a negative reaction from some gamers on social media though.

WIRED spoke with Bloomberg's chief technology officer about the big, chatbot-style changes coming to the iconic platform for traders. For its famous intractability, the Bloomberg Terminal has long inspired devotion, bordering on obsession . Among traders, the ability to chart a path through the software's dizzying scrolls of numbers and text to isolate far-flung information is the mark of a seasoned professional. But as a greater mass of data is fed into the Terminal--not only earnings and asset prices, but weather forecasts, shipping logs, factory locations, consumer spending patterns, private loans, and so on--valuable information is being lost. "It has become more and more untenable," says Shawn Edwards, chief technology officer at Bloomberg.

Although online handwriting verification has made great progress recently, the verification performances are still far behind the real usage owing to the small scale of the datasets as well as the limited biometric mediums. Therefore, this paper proposes a new handwriting verification benchmark dataset named Multimodal Signature and Digit String (MSDS), which consists of two subsets: MSDS-ChS (Chinese Signatures) and MSDS-TDS (Token Digit Strings), contributed by 402 users, with 20 genuine samples and 20 skilled forgeries per user per subset. MSDS-ChS consists of handwritten Chinese signatures, which, to the best of our knowledge, is the largest publicly available Chinese signature dataset for handwriting verification, at least eight times larger than existing online datasets. Meanwhile, MSDS-TDS consists of handwritten Token Digit Strings, i.e, the actual phone numbers of users, which have not been explored yet. Extensive experiments with different baselines are respectively conducted for MSDS-ChS and MSDS-TDS. Surprisingly, verification performances of state-of-the-art methods on MSDS-TDS are generally better than those on MSDS-ChS, which indicates that the handwritten Token Digit String could be a more effective biometric than handwritten Chinese signature. This is a promising discovery that could inspire us to explore new biometric traits.