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The cryptocurrency market is volatile, non-stationary and non-continuous. Together with liquid derivatives markets, this poses a unique opportunity to study risk management, especially the hedging of options, in a turbulent market. We study the hedge behaviour and effectiveness for the class of affine jump diffusion models and infinite activity Levy processes. First, market data is calibrated to stochastic volatility inspired (SVI)-implied volatility surfaces to price options. To cover a wide range of market dynamics, we generate Monte Carlo price paths using an SVCJ model (stochastic volatility with correlated jumps), a close-to-actual-market GARCH-filtered kernel density estimation as well as a historical backtest. In all three settings, options are dynamically hedged with Delta, Delta-Gamma, Delta-Vega and Minimum Variance strategies. Including a wide range of market models allows to understand the trade-off in the hedge performance between complete, but overly parsimonious models, and more complex, but incomplete models. The calibration results reveal a strong indication for stochastic volatility, low jump frequency and evidence of infinite activity. Short-dated options are less sensitive to volatility or Gamma hedges. For longer-dated options, tail risk is consistently reduced by multiple-instrument hedges, in particular by employing complete market models with stochastic volatility.

Most published work on differential privacy (DP) focuses exclusively on meeting privacy constraints, by adding to the query noise with a pre-specified parametric distribution model, typically with one or two degrees of freedom. The accuracy of the response and its utility to the intended use are frequently overlooked. Considering that several database queries are categorical in nature (e.g., a label, a ranking, etc.), or can be quantized, the parameters that define the randomized mechanism's distribution are finite. Thus, it is reasonable to search through numerical optimization for the probability masses that meet the privacy constraints while minimizing the query distortion. Considering the modulo summation of random noise as the DP mechanism, the goal of this paper is to introduce a tractable framework to design the optimum noise probability mass function (PMF) for database queries with a discrete and finite set, optimizing with an expected distortion metric for a given $(\epsilon,\delta)$. We first show that the optimum PMF can be obtained by solving a mixed integer linear program (MILP). Then, we derive closed-form solutions for the optimum PMF that minimize the probability of error for two special cases. We show numerically that the proposed optimal mechanisms significantly outperform the state-of-the-art.

Efficient data transfers over high-speed, long-distance shared networks require proper utilization of available network bandwidth. Using parallel TCP streams enables an application to utilize network parallelism and can improve transfer throughput; however, finding the optimum number of parallel TCP streams is challenging due to nondeterministic background traffic sharing the same network. Additionally, the non-stationary, multi-objectiveness, and partially-observable nature of network signals in the host systems add extra complexity in finding the current network condition. In this work, we present a novel approach to finding the optimum number of parallel TCP streams using deep reinforcement learning (RL). We devise a learning-based algorithm capable of generalizing different network conditions and utilizing the available network bandwidth intelligently. Contrary to rule-based heuristics that do not generalize well in unknown network scenarios, our RL-based solution can dynamically discover and adapt the parallel TCP stream numbers to maximize the network bandwidth utilization without congesting the network and ensure fairness among contending transfers. We extensively evaluated our RL-based algorithm's performance, comparing it with several state-of-the-art online optimization algorithms. The results show that our RL-based algorithm can find near-optimal solutions 40% faster while achieving up to 15% higher throughput. We also show that, unlike a greedy algorithm, our devised RL-based algorithm can avoid network congestion and fairly share the available network resources among contending transfers.

We consider estimation under model misspecification where there is a model mismatch between the underlying system, which generates the data, and the model used during estimation. We propose a model misspecification framework which enables a joint treatment of the model misspecification types of having fake features as well as incorrect covariance assumptions on the unknowns and the noise. We present a decomposition of the output error into components that relate to different subsets of the model parameters corresponding to underlying, fake and missing features. Here, fake features are features which are included in the model but are not present in the underlying system. Under this framework, we characterize the estimation performance and reveal trade-offs between the number of samples, number of fake features, and the possibly incorrect noise level assumption. In contrast to existing work focusing on incorrect covariance assumptions or missing features, fake features is a central component of our framework. Our results show that fake features can significantly improve the estimation performance, even though they are not correlated with the features in the underlying system. In particular, we show that the estimation error can be decreased by including more fake features in the model, even to the point where the model is overparametrized, i.e., the model contains more unknowns than observations.

Online Class Incremental learning (CIL) is a challenging setting in Continual Learning (CL), wherein data of new tasks arrive in incoming streams and online learning models need to handle incoming data streams without revisiting previous ones. Existing works used a single centroid adapted with incoming data streams to characterize a class. This approach possibly exposes limitations when the incoming data stream of a class is naturally multimodal. To address this issue, in this work, we first propose an online mixture model learning approach based on nice properties of the mature optimal transport theory (OT-MM). Specifically, the centroids and covariance matrices of the mixture model are adapted incrementally according to incoming data streams. The advantages are two-fold: (i) we can characterize more accurately complex data streams and (ii) by using centroids for each class produced by OT-MM, we can estimate the similarity of an unseen example to each class more reasonably when doing inference. Moreover, to combat the catastrophic forgetting in the CIL scenario, we further propose Dynamic Preservation. Particularly, after performing the dynamic preservation technique across data streams, the latent representations of the classes in the old and new tasks become more condensed themselves and more separate from each other. Together with a contraction feature extractor, this technique facilitates the model in mitigating the catastrophic forgetting. The experimental results on real-world datasets show that our proposed method can significantly outperform the current state-of-the-art baselines.

For basic machine learning problems, expected error is used to evaluate model performance. Since the distribution of data is usually unknown, we can make simple hypothesis that the data are sampled independently and identically distributed (i.i.d.) and the mean value of loss function is used as the empirical risk by Law of Large Numbers (LLN). This is known as the Monte Carlo method. However, when LLN is not applicable, such as imbalanced data problems, empirical risk will cause overfitting and might decrease robustness and generalization ability. Inspired by the framework of nonlinear expectation theory, we substitute the mean value of loss function with the maximum value of subgroup mean loss. We call it nonlinear Monte Carlo method. In order to use numerical method of optimization, we linearize and smooth the functional of maximum empirical risk and get the descent direction via quadratic programming. With the proposed method, we achieve better performance than SOTA backbone models with less training steps, and more robustness for basic regression and imbalanced classification tasks.

Change point estimation is often formulated as a search for the maximum of a gain function describing improved fits when segmenting the data. Searching through all candidates requires $O(n)$ evaluations of the gain function for an interval with $n$ observations. If each evaluation is computationally demanding (e.g. in high-dimensional models), this can become infeasible. Instead, we propose optimistic search methods with $O(\log n)$ evaluations exploiting specific structure of the gain function. Towards solid understanding of our strategy, we investigate in detail the $p$-dimensional Gaussian changing means setup, including high-dimensional scenarios. For some of our proposals, we prove asymptotic minimax optimality for detecting change points and derive their asymptotic localization rate. These rates (up to a possible log factor) are optimal for the univariate and multivariate scenarios, and are by far the fastest in the literature under the weakest possible detection condition on the signal-to-noise ratio in the high-dimensional scenario. Computationally, our proposed methodology has the worst case complexity of $O(np)$, which can be improved to be sublinear in $n$ if some a-priori knowledge on the length of the shortest segment is available. Our search strategies generalize far beyond the theoretically analyzed setup. We illustrate, as an example, massive computational speedup in change point detection for high-dimensional Gaussian graphical models.

In this paper we address the solution of the popular Wordle puzzle, using new reinforcement learning methods, which apply more generally to adaptive control of dynamic systems and to classes of Partially Observable Markov Decision Process (POMDP) problems. These methods are based on approximation in value space and the rollout approach, admit a straightforward implementation, and provide improved performance over various heuristic approaches. For the Wordle puzzle, they yield on-line solution strategies that are very close to optimal at relatively modest computational cost. Our methods are viable for more complex versions of Wordle and related search problems, for which an optimal strategy would be impossible to compute. They are also applicable to a wide range of adaptive sequential decision problems that involve an unknown or frequently changing environment whose parameters are estimated on-line.

Multi-stage ranking pipelines have been a practical solution in modern search systems, where the first-stage retrieval is to return a subset of candidate documents, and latter stages attempt to re-rank those candidates. Unlike re-ranking stages going through quick technique shifts during past decades, the first-stage retrieval has long been dominated by classical term-based models. Unfortunately, these models suffer from the vocabulary mismatch problem, which may block re-ranking stages from relevant documents at the very beginning. Therefore, it has been a long-term desire to build semantic models for the first-stage retrieval that can achieve high recall efficiently. Recently, we have witnessed an explosive growth of research interests on the first-stage semantic retrieval models. We believe it is the right time to survey current status, learn from existing methods, and gain some insights for future development. In this paper, we describe the current landscape of the first-stage retrieval models under a unified framework to clarify the connection between classical term-based retrieval methods, early semantic retrieval methods and neural semantic retrieval methods. Moreover, we identify some open challenges and envision some future directions, with the hope of inspiring more researches on these important yet less investigated topics.

With the rapid increase of large-scale, real-world datasets, it becomes critical to address the problem of long-tailed data distribution (i.e., a few classes account for most of the data, while most classes are under-represented). Existing solutions typically adopt class re-balancing strategies such as re-sampling and re-weighting based on the number of observations for each class. In this work, we argue that as the number of samples increases, the additional benefit of a newly added data point will diminish. We introduce a novel theoretical framework to measure data overlap by associating with each sample a small neighboring region rather than a single point. The effective number of samples is defined as the volume of samples and can be calculated by a simple formula $(1-\beta^{n})/(1-\beta)$, where $n$ is the number of samples and $\beta \in [0,1)$ is a hyperparameter. We design a re-weighting scheme that uses the effective number of samples for each class to re-balance the loss, thereby yielding a class-balanced loss. Comprehensive experiments are conducted on artificially induced long-tailed CIFAR datasets and large-scale datasets including ImageNet and iNaturalist. Our results show that when trained with the proposed class-balanced loss, the network is able to achieve significant performance gains on long-tailed datasets.