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We investigate how and when to diversify capital over assets, i.e., the portfolio selection problem, from a signal processing perspective. To this end, we first construct portfolios that achieve the optimal expected growth in i.i.d.…

In the portfolio multiobjective optimization framework, we propose to compare and choose, among all feasible asset portfolios of a given market, the one that maximizes the product of the distances between its values of risk and gain and…

This paper addresses the portfolio selection problem for nonlinear law-dependent preferences in continuous time, which inherently exhibit time inconsistency. Employing the method of stochastic maximum principle, we establish verification…

We study the privatization of distributed learning and optimization strategies. We focus on differential privacy schemes and study their effect on performance. We show that the popular additive random perturbation scheme degrades…

Biased stochastic estimators, such as finite-differences for noisy gradient estimation, often contain parameters that need to be properly chosen to balance impacts from the bias and the variance. While the optimal order of these parameters…

The standard approach for constructing a Mean-Variance portfolio involves estimating parameters for the model using collected samples. However, since the distribution of future data may not resemble that of the training set, the…

We study the behavior of optimal ridge regularization and optimal ridge risk for out-of-distribution prediction, where the test distribution deviates arbitrarily from the train distribution. We establish general conditions that determine…

We find economically and statistically significant gains when using machine learning for portfolio allocation between the market index and risk-free asset. Optimal portfolio rules for time-varying expected returns and volatility are…

We develop an approach to risk minimization and stochastic optimization that provides a convex surrogate for variance, allowing near-optimal and computationally efficient trading between approximation and estimation error. Our approach…

Randomized smoothing is the current state-of-the-art method for producing provably robust classifiers. While randomized smoothing typically yields robust $\ell_2$-ball certificates, recent research has generalized provable robustness to…

We present a parsimonious neural network approach, which does not rely on dynamic programming techniques, to solve dynamic portfolio optimization problems subject to multiple investment constraints. The number of parameters of the…

This paper introduces and examines numerical approximation schemes for computing risk budgeting portfolios associated to positive homogeneous and sub-additive risk measures. We employ Mirror Descent algorithms to determine the optimal risk…

Classification and Regression Trees (CARTs) are off-the-shelf techniques in modern Statistics and Machine Learning. CARTs are traditionally built by means of a greedy procedure, sequentially deciding the splitting predictor variable(s) and…

Investment returns naturally reside on irregular domains, however, standard multivariate portfolio optimization methods are agnostic to data structure. To this end, we investigate ways for domain knowledge to be conveniently incorporated…

We apply numerical dynamic programming techniques to solve discrete-time multi-asset dynamic portfolio optimization problems with proportional transaction costs and shorting/borrowing constraints. Examples include problems with multiple…

Modern stochastic optimization methods often rely on uniform sampling which is agnostic to the underlying characteristics of the data. This might degrade the convergence by yielding estimates that suffer from a high variance. A possible…

This paper introduces a drift optimization model of stochastic optimization problems driven by regulated stochastic processes. A broad range of problems across operations research, machine learning, and statistics can be viewed as…

We study the generation of dependent random numbers in a distributed fashion in order to enable privatized distributed learning by networked agents. We propose a method that we refer to as local graph-homomorphic processing; it relies on…

Growth-optimal portfolios are guaranteed to accumulate higher wealth than any other investment strategy in the long run. However, they tend to be risky in the short term. For serially uncorrelated markets, similar portfolios with more…

Random forests remain among the most popular off-the-shelf supervised machine learning tools with a well-established track record of predictive accuracy in both regression and classification settings. Despite their empirical success as well…