亚洲男人的天堂2018av,欧美草比,久久久久久免费视频精选,国色天香在线看免费,久久久久亚洲av成人片仓井空

In this paper, we propose a new covering technique localized for the trajectories of SGD. This localization provides an algorithm-specific complexity measured by the covering number, which can have dimension-independent cardinality in contrast to standard uniform covering arguments that result in exponential dimension dependency. Based on this localized construction, we show that if the objective function is a finite perturbation of a piecewise strongly convex and smooth function with $P$ pieces, i.e. non-convex and non-smooth in general, the generalization error can be upper bounded by $O(\sqrt{(\log n\log(nP))/n})$, where $n$ is the number of data samples. In particular, this rate is independent of dimension and does not require early stopping and decaying step size. Finally, we employ these results in various contexts and derive generalization bounds for multi-index linear models, multi-class support vector machines, and $K$-means clustering for both hard and soft label setups, improving the known state-of-the-art rates.

Stock prices move as piece-wise trending fluctuation rather than a purely random walk. Traditionally, the prediction of future stock movements is based on the historical trading record. Nowadays, with the development of social media, many active participants in the market choose to publicize their strategies, which provides a window to glimpse over the whole market's attitude towards future movements by extracting the semantics behind social media. However, social media contains conflicting information and cannot replace historical records completely. In this work, we propose a multi-modality attention network to reduce conflicts and integrate semantic and numeric features to predict future stock movements comprehensively. Specifically, we first extract semantic information from social media and estimate their credibility based on posters' identity and public reputation. Then we incorporate the semantic from online posts and numeric features from historical records to make the trading strategy. Experimental results show that our approach outperforms previous methods by a significant margin in both prediction accuracy (61.20\%) and trading profits (9.13\%). It demonstrates that our method improves the performance of stock movements prediction and informs future research on multi-modality fusion towards stock prediction.

In narrow spaces, motion planning based on the traditional hierarchical autonomous system could cause collisions due to mapping, localization, and control noises. Additionally, it is disabled when mapless. To tackle these problems, we leverage deep reinforcement learning which is verified to be effective in self-decision-making, to self-explore in narrow spaces without a map while avoiding collisions. Specifically, based on our Ackermann-steering rectangular-shaped ZebraT robot and its Gazebo simulator, we propose the rectangular safety region to represent states and detect collisions for rectangular-shaped robots, and a carefully crafted reward function for reinforcement learning that does not require the destination information. Then we benchmark five reinforcement learning algorithms including DDPG, DQN, SAC, PPO, and PPO-discrete, in a simulated narrow track. After training, the well-performed DDPG and DQN models can be transferred to three brand new simulated tracks, and furthermore to three real-world tracks.

The significant presence of demand charges in electric bills motivates large-load customers to utilize energy storage to reduce the peak procurement from the grid. We herein study the problem of energy storage allocation for peak minimization, under the online setting where irrevocable decisions are sequentially made without knowing future demands. The problem is uniquely challenging due to (i) the coupling of online decisions across time imposed by the inventory constraints and (ii) the noncumulative nature of the peak procurement. We apply the CR-Pursuit framework and address the challenges unique to our minimization problem to design an online algorithm achieving the optimal competitive ratio (CR) among all online algorithms. We show that the optimal CR can be computed in polynomial time by solving a linear number of linear-fractional problems. More importantly, we generalize our approach to develop an \emph{anytime-optimal} online algorithm that achieves the best possible CR at any epoch, given the inputs and online decisions so far. The algorithm retains the optimal worst-case performance and attains adaptive average-case performance. Trace-driven simulations show that our algorithm can decrease the peak demand by an extra 19% compared to baseline alternatives under typical settings.

The $h$-index is a metric used to measure the impact of a user in a publication setting, such as a member of a social network with many highly liked posts or a researcher in an academic domain with many highly cited publications. Specifically, the $h$-index of a user is the largest integer $h$ such that at least $h$ publications of the user have at least $h$ units of positive feedback. We design an algorithm that, given query access to the $n$ publications of a user and each publication's corresponding positive feedback number, outputs a $(1\pm \varepsilon)$-approximation of the $h$-index of this user with probability at least $1-\delta$ in time \[ O(\frac{n \cdot \ln{(1/\delta)}}{\varepsilon^2 \cdot h}), \] where $h$ is the actual $h$-index which is unknown to the algorithm a-priori. We then design a novel lower bound technique that allows us to prove that this bound is in fact asymptotically optimal for this problem in all parameters $n,h,\varepsilon,$ and $\delta$. Our work is one of the first in sublinear time algorithms that addresses obtaining asymptotically optimal bounds, especially in terms of the error and confidence parameters. As such, we focus on designing novel techniques for this task. In particular, our lower bound technique seems quite general -- to showcase this, we also use our approach to prove an asymptotically optimal lower bound for the problem of estimating the number of triangles in a graph in sublinear time, which now is also optimal in the error and confidence parameters. This result improves upon prior lower bounds of Eden, Levi, Ron, and Seshadhri (FOCS'15) for this problem, as well as multiple follow-ups that extended this lower bound to other subgraph counting problems.

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 \cite{lei2021stability}. 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.

Privacy has become a major concern in machine learning. In fact, the federated learning is motivated by the privacy concern as it does not allow to transmit the private data but only intermediate updates. However, federated learning does not always guarantee privacy-preservation as the intermediate updates may also reveal sensitive information. In this paper, we give an explicit information-theoretical analysis of a federated expectation maximization algorithm for Gaussian mixture model and prove that the intermediate updates can cause severe privacy leakage. To address the privacy issue, we propose a fully decentralized privacy-preserving solution, which is able to securely compute the updates in each maximization step. Additionally, we consider two different types of security attacks: the honest-but-curious and eavesdropping adversary models. Numerical validation shows that the proposed approach has superior performance compared to the existing approach in terms of both the accuracy and privacy level.

In this paper, we develop a novel class of linear energy-preserving integrating factor methods for the 2D nonlinear Schr\"odinger equation with wave operator (NLSW), combining the scalar auxiliary variable approach and the integrating factor methods. A second-order scheme is first proposed, which is rigorously proved to be energy-preserving. By using the energy methods, we analyze its optimal convergence in the $H^1$ norm without any restrictions on the grid ratio, where a novel technique and an improved induction argument are proposed to overcome the difficulty posed by the unavailability of a priori $L^\infty$ estimates of numerical solutions. Based on the integrating factor Runge-Kutta methods, we extend the proposed scheme to arbitrarily high order, which is also linear and conservative. Numerical experiments are presented to confirm the theoretical analysis and demonstrate the advantages of the proposed methods.

We study differentially private (DP) stochastic optimization (SO) with data containing outliers and loss functions that are not Lipschitz continuous. To date, the vast majority of work on DP SO assumes that the loss is Lipschitz (i.e. stochastic gradients are uniformly bounded), and their error bounds scale with the Lipschitz parameter of the loss. While this assumption is convenient, it is often unrealistic: in many practical problems where privacy is required, data may contain outliers or be unbounded, causing some stochastic gradients to have large norm. In such cases, the Lipschitz parameter may be prohibitively large, leading to vacuous excess risk bounds. Thus, building on a recent line of work [WXDX20, KLZ22], we make the weaker assumption that stochastic gradients have bounded $k$-th moments for some $k \geq 2$. Compared with works on DP Lipschitz SO, our excess risk scales with the $k$-th moment bound instead of the Lipschitz parameter of the loss, allowing for significantly faster rates in the presence of outliers. For convex and strongly convex loss functions, we provide the first asymptotically optimal excess risk bounds (up to a logarithmic factor). Moreover, in contrast to the prior works [WXDX20, KLZ22], our bounds do not require the loss function to be differentiable/smooth. We also devise an accelerated algorithm that runs in linear time and yields improved (compared to prior works) and nearly optimal excess risk for smooth losses. Additionally, our work is the first to address non-convex non-Lipschitz loss functions satisfying the Proximal-PL inequality; this covers some classes of neural nets, among other practical models. Our Proximal-PL algorithm has nearly optimal excess risk that almost matches the strongly convex lower bound. Lastly, we provide shuffle DP variations of our algorithms, which do not require a trusted curator (e.g. for distributed learning).

Stochastic kriging has been widely employed for simulation metamodeling to predict the response surface of complex simulation models. However, its use is limited to cases where the design space is low-dimensional because, in general, the sample complexity (i.e., the number of design points required for stochastic kriging to produce an accurate prediction) grows exponentially in the dimensionality of the design space. The large sample size results in both a prohibitive sample cost for running the simulation model and a severe computational challenge due to the need to invert large covariance matrices. Based on tensor Markov kernels and sparse grid experimental designs, we develop a novel methodology that dramatically alleviates the curse of dimensionality. We show that the sample complexity of the proposed methodology grows only slightly in the dimensionality, even under model misspecification. We also develop fast algorithms that compute stochastic kriging in its exact form without any approximation schemes. We demonstrate via extensive numerical experiments that our methodology can handle problems with a design space of more than 10,000 dimensions, improving both prediction accuracy and computational efficiency by orders of magnitude relative to typical alternative methods in practice.