13 research outputs found
Fast projections onto mixed-norm balls with applications
Joint sparsity offers powerful structural cues for feature selection,
especially for variables that are expected to demonstrate a "grouped" behavior.
Such behavior is commonly modeled via group-lasso, multitask lasso, and related
methods where feature selection is effected via mixed-norms. Several mixed-norm
based sparse models have received substantial attention, and for some cases
efficient algorithms are also available. Surprisingly, several constrained
sparse models seem to be lacking scalable algorithms. We address this
deficiency by presenting batch and online (stochastic-gradient) optimization
methods, both of which rely on efficient projections onto mixed-norm balls. We
illustrate our methods by applying them to the multitask lasso. We conclude by
mentioning some open problems.Comment: Preprint of paper under revie
Spatiotemporally Constrained Action Space Attacks on Deep Reinforcement Learning Agents
Robustness of Deep Reinforcement Learning (DRL) algorithms towards
adversarial attacks in real world applications such as those deployed in
cyber-physical systems (CPS) are of increasing concern. Numerous studies have
investigated the mechanisms of attacks on the RL agent's state space.
Nonetheless, attacks on the RL agent's action space (AS) (corresponding to
actuators in engineering systems) are equally perverse; such attacks are
relatively less studied in the ML literature. In this work, we first frame the
problem as an optimization problem of minimizing the cumulative reward of an RL
agent with decoupled constraints as the budget of attack. We propose a
white-box Myopic Action Space (MAS) attack algorithm that distributes the
attacks across the action space dimensions. Next, we reformulate the
optimization problem above with the same objective function, but with a
temporally coupled constraint on the attack budget to take into account the
approximated dynamics of the agent. This leads to the white-box Look-ahead
Action Space (LAS) attack algorithm that distributes the attacks across the
action and temporal dimensions. Our results shows that using the same amount of
resources, the LAS attack deteriorates the agent's performance significantly
more than the MAS attack. This reveals the possibility that with limited
resource, an adversary can utilize the agent's dynamics to malevolently craft
attacks that causes the agent to fail. Additionally, we leverage these attack
strategies as a possible tool to gain insights on the potential vulnerabilities
of DRL agents.Comment: Version 2 with supplementary material
Multitask Online Mirror Descent
We introduce and analyze MT-OMD, a multitask generalization of Online Mirror
Descent (OMD) which operates by sharing updates between tasks. We prove that
the regret of MT-OMD is of order , where
is the task variance according to the geometry induced by the
regularizer, is the number of tasks, and is the time horizon. Whenever
tasks are similar, that is , our method improves upon the
bound obtained by running independent OMDs on each task. We further
provide a matching lower bound, and show that our multitask extensions of
Online Gradient Descent and Exponentiated Gradient, two major instances of OMD,
enjoy closed-form updates, making them easy to use in practice. Finally, we
present experiments on both synthetic and real-world datasets supporting our
findings
Scalable Randomized Kernel Methods for Multiview Data Integration and Prediction
We develop scalable randomized kernel methods for jointly associating data
from multiple sources and simultaneously predicting an outcome or classifying a
unit into one of two or more classes. The proposed methods model nonlinear
relationships in multiview data together with predicting a clinical outcome and
are capable of identifying variables or groups of variables that best
contribute to the relationships among the views. We use the idea that random
Fourier bases can approximate shift-invariant kernel functions to construct
nonlinear mappings of each view and we use these mappings and the outcome
variable to learn view-independent low-dimensional representations. Through
simulation studies, we show that the proposed methods outperform several other
linear and nonlinear methods for multiview data integration. When the proposed
methods were applied to gene expression, metabolomics, proteomics, and
lipidomics data pertaining to COVID-19, we identified several molecular
signatures forCOVID-19 status and severity. Results from our real data
application and simulations with small sample sizes suggest that the proposed
methods may be useful for small sample size problems. Availability: Our
algorithms are implemented in Pytorch and interfaced in R and would be made
available at: https://github.com/lasandrall/RandMVLearn.Comment: 24 pages, 5 figures, 4 table
Efficient Primal-Dual Algorithms for Large-Scale Multiclass Classification
We develop efficient algorithms to train -regularized linear classifiers with large dimensionality of the feature space, number of classes , and sample size . Our focus is on a special class of losses that includes, in particular, the multiclass hinge and logistic losses. Our approach combines several ideas: (i) passing to the equivalent saddle-point problem with a quasi-bilinear objective; (ii) applying stochastic mirror descent with a proper choice of geometry which guarantees a favorable accuracy bound; (iii) devising non-uniform sampling schemes to approximate the matrix products. In particular, for the multiclass hinge loss we propose a \textit{sublinear} algorithm with iterations performed in arithmetic operations