Related papers: $L_p$ regularized portfolio optimization
Linearly parametrized models are widely used in control and signal processing, with the least-squares (LS) estimate being the archetypical solution. When the input is insufficiently exciting, the LS problem may be unsolvable or numerically…
Inspired by regularization techniques in statistics and machine learning, we study complementary composite minimization in the stochastic setting. This problem corresponds to the minimization of the sum of a (weakly) smooth function endowed…
Given a weighted graph with $N$ vertices, consider a real-valued regression problem in a semi-supervised setting, where one observes $n$ labeled vertices, and the task is to label the remaining ones. We present a theoretical study of…
We revisit mean-risk portfolio selection in a one-period financial market where risk is quantified by a positively homogeneous risk measure $\rho$. We first show that under mild assumptions, the set of optimal portfolios for a fixed return…
We present algorithms for efficiently learning regularizers that improve generalization. Our approach is based on the insight that regularizers can be viewed as upper bounds on the generalization gap, and that reducing the slack in the…
Constant product markets with concentrated liquidity (CL) are the most popular type of automated market makers. In this paper, we characterise the continuous-time wealth dynamics of strategic LPs who dynamically adjust their range of…
The $\ell_p$ linear regression problem is to minimize $f(x)=||Ax-b||_p$ over $x\in\mathbb{R}^d$, where $A\in\mathbb{R}^{n\times d}$, $b\in \mathbb{R}^n$, and $p>0$. To avoid overfitting and bound $||x||_2$, the constrained $\ell_p$…
This work revisits a recent finding by the first author concerning the local convergence of a regularized scalar conservation law. We significantly improve the original statement by establishing a global convergence result within the…
Randomized smoothing has shown promising certified robustness against adversaries in classification tasks. Despite such success with only zeroth-order access to base models, randomized smoothing has not been extended to a general form of…
We use a replica approach to deal with portfolio optimization problems. A given risk measure is minimized using empirical estimates of asset values correlations. We study the phase transition which happens when the time series is too short…
We extend Relative Robust Portfolio Optimisation models to allow portfolios to optimise their distance to a set of benchmarks. Portfolio managers are also given the option of computing regret in a way which is more in line with market…
We develop a family of accelerated stochastic algorithms that minimize sums of convex functions. Our algorithms improve upon the fastest running time for empirical risk minimization (ERM), and in particular linear least-squares regression,…
Safe reinforcement learning (safe RL) aims to respect safety requirements while optimizing long-term performance. In many practical applications, however, the problem involves an infinite number of constraints, known as semi-infinite safe…
Reinforcement learning (RL) based investment strategies have been widely adopted in portfolio management (PM) in recent years. Nevertheless, most RL-based approaches may often emphasize on pursuing returns while ignoring the risks of the…
We show that coherent risk measures are ineffective in curbing the behaviour of investors with limited liability or excessive tail-risk seeking behaviour if the market admits statistical arbitrage opportunities which we term…
Prediction sets can wrap around any ML model to cover unknown test outcomes with a guaranteed probability. Yet, it remains unclear how to use them optimally for downstream decision-making. Here, we propose a decision-theoretic framework…
In this effort, we consider the impact of regularization on the diversity of actions taken by policies generated from reinforcement learning agents trained using a policy gradient. Policy gradient agents are prone to entropy collapse, which…
It is important for a portfolio manager to estimate and analyze recent portfolio volatility to keep the portfolio's risk within limit. Though the number of financial instruments in the portfolio can be very large, sometimes more than…
While the idea of robust dynamic programming (DP) is compelling for systems affected by uncertainty, addressing worst-case disturbances generally results in excessive conservatism. This paper introduces a method for constructing control…
Regularization is widely used in statistics and machine learning to prevent overfitting and gear solution towards prior information. In general, a regularized estimation problem minimizes the sum of a loss function and a penalty term. The…