New stochastic algorithms solve DC functions and non-convex problems efficiently.
problem Solving non-convex, non-smooth, and non-differentiable functions efficiently.
method Proposed new stochastic optimization algorithms for DC functions and non-convex problems.
result First non-asymptotic convergence for non-convex optimization with general non-convex non-differentiable regularizers.
Investigates risk measures for DC pension decumulation.
problem Develop optimal decumulation strategies for DC plan holders.
method Formulates decumulation as a control problem, studies risk measures (expected shortfall, linear shortfall, probability of shortfall).
result Optimal controls for expected reward and expected shortfall are identical to those for expected reward and linear shortfall.
Sparse optimization refers to an optimization problem involving the zero-norm in objective or constraints. In this paper, nonconvex approximation approaches for sparse optimization have been studied with a unifying point of view in DC (Difference of Convex functions) programming framework. Considering a common DC appro…
This paper tackles multi-marginal optimal transport problems using DC programming.
problem Multi-marginal optimal transport problems in machine learning.
method Promoting structural information in MMOT leads to a DC programming problem.
result Solutions from DC optimization are as qualitative as current methods.
New method uses momentum to converge in DC optimization with small batches.
problem Lack of convergence properties for stochastic difference-of-convex optimization with small batch sizes.
method Introduces momentum to enable convergence under standard assumptions for any batch size.
result Proves convergence of the algorithm under smoothness and bounded variance assumptions.
This paper optimizes DC pension plan investments using O-U process and loan.
problem Optimizing investment strategy for DC pension plans under specific market conditions.
method Dynamic programming and Hamilton-Jacobi-Bellman equation to derive optimal investment strategy.
result Explicit expression for optimal investment strategy derived.
New algorithms improve submodular minimization via DC programming.
problem Minimizing the difference of two submodular functions.
method Introducing variants of the DC algorithm (DCA) and its complete form (CDCA) for DC programs corresponding to DS minimization.
result Our algorithms outperform existing baselines on speech corpus selection and feature selection.
SDF-Bayes finds safe drug combinations safely, balancing optimism and caution.
problem Finding safe drug combinations in clinical trials with multiple drugs and patient heterogeneity.
method SDF-Bayes uses Bayesian statistics to choose the most likely MTD while ensuring safety constraints.
result SDF-Bayes outperforms existing methods in both accuracy and safety for drug combination trials.
Paper optimizes DC pension fund management with VaR and relative performance constraints.
problem Optimizing DC pension fund performance under VaR and relative performance constraints.
method Introduced an auxiliary process to transform the problem into a self-financing problem, combined linearization, Lagrange dual, martingale, and concavification methods.
result Explicit investment strategies obtained for certain penalty and reward functions.
Paper proposes iLPA for solving DC composite optimization problems, with applications to matrix completion with outliers.
problem Solving nonconvex and nonsmooth DC composite optimization problems.
method Inexact linearized proximal algorithm (iLPA) for DC composite optimization problems.
result The iLPA achieves local R-linear convergence rate under the Kurdyka-Łöjasiewicz property.
Joint blind source separation (J-BSS) is an emerging data-driven technique for multi-set data-fusion. In this paper, J-BSS is addressed from a tensorial perspective. We show how, by using second-order multi-set statistics in J-BSS, a specific double coupled canonical polyadic decomposition (DC-CPD) problem can be formu…
ALMAB-DC optimizes expensive black-box experiments using active learning and distributed computing.
problem Efficiently optimizing expensive, gradient-free objectives in computational statistics and machine learning.
method Combines active learning, multi-armed bandits, and distributed asynchronous computing.
result Achieves lower simple regret and superior performance in various tasks compared to non-ALMAB baselines.
Paper proposes DC functions for better regularization of inverse problems with theoretical guarantees.
problem Improving regularization for ill-posed inverse problems.
method Introduces difference-of-convex (DC) functions and uses them with optimization algorithms like DCA and PSM.
result DC functions yield improved performance and theoretical guarantees compared to weakly convex functions.
Investment strategy for DC pension plan with inflation risk and tail VaR constraint.
problem Maximizing terminal wealth for pension member with tail VaR constraint.
method Lagrange method and quantile optimization techniques.
result Optimal investment strategy and output in closed-form derived.
DCA algorithm applied to SVR with RBF kernel for nonconvex optimization.
problem Nonconvex optimization of SVR with Gaussian RBF kernel.
method DC algorithm with analytical DC decomposition of SVR objective.
result Convergence properties of DCA on RBF-SVR can be assessed through C α ρ C_αρ C α ρ . A new DC programming approach improves RBM training efficiency.
problem Improving the training efficiency of Restricted Boltzmann Machines (RBMs).
method Formulated a stochastic DC programming approach to minimize RBM log-likelihood.
result The new algorithm achieves higher log-likelihood more rapidly with the same computational budget.
We propose a DC proximal Newton algorithm for solving nonconvex regularized sparse learning problems in high dimensions. Our proposed algorithm integrates the proximal Newton algorithm with multi-stage convex relaxation based on the difference of convex (DC) programming, and enjoys both strong computational and statist…
New method uses DC functions for piecewise linear regression.
problem Regression with piecewise linear constraints.
method Estimates piecewise linear convex functions using a difference of convex functions.
result Method achieves close to minimax statistical risk and comparable performance to existing methods.
Paper tackles non-convex inf-projection problems with stochastic optimization.
problem Non-convex and possibly non-smooth inf-projection minimization problems.
method Developed stochastic algorithms for finding (nearly) stationary solutions.
result Established first-order convergence for non-convex inf-projection problems.
Unified framework for scalable black-box optimization.
problem Expensive black-box evaluations in scientific and engineering domains.
method Integrates active learning, multi-armed bandits, and distributed computing.
result Consistently outperforms state-of-the-art black-box optimizers.
This work builds a sensor graph from DC sensors for anomaly detection.
problem Anomaly detection in data centers with complex sensor relationships.
method Data-driven pipeline (ts2graph) to build a sensor graph from sensor time series.
result Graph neural network (GNN) outperforms existing methods by 2-3 times in anomaly detection.
Proposes DC-S3GD for efficient large-scale decentralized neural network training.
problem Training large-scale decentralized neural networks efficiently.
method Decentralized stale-synchronous version of DC-ASGD with gradient correction.
result Achieves state-of-the-art results in training Convolutional Neural Networks.
DC-NAS improves neural architecture search by clustering and evaluating sub-networks.
problem Inaccurate evaluation of neural architectures in large search spaces.
method Divide-and-Conquer approach: feature representation, clustering, and evaluation of clusters.
result Achieved 75.1% top-1 accuracy on ImageNet, surpassing state-of-the-art methods.
A new algorithm solves signed Fréchet regression on manifolds with bounded curvature.
problem Signed Fréchet regression on Riemannian manifolds with bounded curvature.
method Proximal DC algorithm (FRIDA) for computing signed Fréchet regression fits.
result Existence and interiority of minimizers, strong convexity of proximal subproblems, and convergence to stationary points.
Study optimal asset allocation for DC plans with inflation and mortality risks.
problem Maximizing expected utility from terminal wealth in a pension plan with inflation and mortality risks.
method Closed-form solutions using a sufficient maximum principle approach for a problem with partial information.
result Closed-form solutions for asset allocation problem.
This paper reports applications of Difference of Convex functions (DC) programming to Learning from Demonstrations (LfD) and Reinforcement Learning (RL) with expert data. This is made possible because the norm of the Optimal Bellman Residual (OBR), which is at the heart of many RL and LfD algorithms, is DC. Improvement…
DC-Prophet predicts catastrophic server failures in datacenters.
problem Forecasting catastrophic machine failures in datacenters.
method Two-stage framework based on One-Class Support Vector Machine and Random Forest.
result DC-Prophet achieves an AUC of 0.93 and F3-score of 0.88 in predicting the next machine failure.
We introduce a novel algorithm for solving learning problems where both the loss function and the regularizer are non-convex but belong to the class of difference of convex (DC) functions. Our contribution is a new general purpose proximal Newton algorithm that is able to deal with such a situation. The algorithm consi…
In this paper, we extend the DC Calculus introduced by Perelman on finite dimensional Alexandrov spaces with curvature bounded below. Among other things, our results allow us to define the Hessian and the Laplacian of DC functions (including distance functions as a particular instance) as a measure-valued tensor and a …
Proposes a new model for diversified interactive recommendation.
problem Previous methods focus on optimizing recommendation accuracy, ignoring diversity.
method DC 2 ^2 2 B model using determinantal point process and Thompson sampling-based variational Bayesian inference. result Demonstrates effectiveness of the proposed method through extensive experiments.
DC-Check helps guide ML development by considering data-centric aspects.
problem Lack of standardized framework for data-centric considerations in ML.
method DC-Check is a checklist-style framework for data-centric AI at ML pipeline stages.
result Promotes thoughtfulness and transparency in ML development.
A new algorithm D C 2 DC^2 D C 2 for large-scale kernel learning and clustering.
problem Efficiently handle large-scale kernel learning and clustering problems.
method Divide-and-conquer approach using recursive random projections for data partition and compression.
result Achieves clustering accuracy comparable to fast approximate spectral clustering algorithms with lower running time.
Estimates Markov chains from data with a non-convex rank-constrained approach.
problem Estimating low-rank Markov chains from empirical data.
method Rank-constrained likelihood maximization and DC programming.
result The proposed estimator achieves better empirical performance than other methods.
X-DC improves speech separation by making DNNs more interpretable.
problem Black-box nature of DNNs in speech separation tasks.
method Introduces X-DC, a DNN architecture that interprets as spectrogram template fitting followed by Wiener filtering.
result X-DC achieves comparable speech separation performance to DC but with enhanced interpretability.
A new nonparametric approach for system identification has been recently proposed where the impulse response is modeled as the realization of a zero-mean Gaussian process whose covariance (kernel) has to be estimated from data. In this scheme, quality of the estimates crucially depends on the parametrization of the cov…
This paper tackles noise in raw datasets to improve representation learning efficiency.
problem Noise in real-world datasets degrades representation learning quality.
method Proposes denoising Cosine-Similarity (dCS) loss to learn robust representations.
result Empirical results show the dCS loss outperforms baseline objective functions.
A novel approach for federated learning over-the-air computation to reduce latency and improve privacy.
problem Low-latency and privacy issues in edge machine learning for intelligent devices.
method Over-the-air computation and sparse-low-rank optimization for efficient global model aggregation.
result Efficient global model aggregation with low latency and improved privacy.
New method estimates optimal dose intervals for personalized treatment.
problem Learning optimal dose intervals from observational data.
method Probability dose interval (PDI) method using DC algorithm.
result Consistent policy with risk converging to best-in-class at root-n rate.
S3VDC improves DC methods for scalability, stability, and simplicity.
problem Poor scalability, instability, and lack of simplicity in DC methods.
method Four algorithmic improvements: initial γ γ γ -training, periodic β β β -annealing, mini-batch GMM initialization, and inverse min-max transform. S3VDC incorporates all improvements. result S3VDC outperforms state-of-the-art methods on benchmark and industrial datasets.
The paper proposes a new method to predict VaR using DCS and generalized distributions.
problem Improving VaR prediction models in financial risk management.
method Dynamic Conditional Score (DCS) model combined with generalized distributions (GD).
result The proposed model outperforms traditional models in high-risk VaR prediction.
FGTSVA improves Thompson Sampling for contextual bandits with optimal variance-aware regret.
problem Optimizing regret bounds for Thompson Sampling in contextual bandits.
method Developed FGTSVA, a variance-aware Thompson Sampling algorithm for contextual bandits with a new decoupling coefficient.
result Achieved optimal regret bound of i l d e O ( d c ⋅ log ∣ F ∣ ∑ t = 1 T σ t 2 + d c ) ilde{O}(\sqrt{\mathrm{dc}\cdot\log|\mathcal{F}|\sum_{t=1}^Tσ_t^2}+\mathrm{dc}) i l d e O ( dc ⋅ log ∣ F ∣ ∑ t = 1 T σ t 2 + dc ) . Paper solves high-order portfolio optimization with cardinality constraint.
problem Solving non-convex cardinality constrained high-order portfolio optimization.
method Transformed cardinality constraint into penalty term, proposed pDCA, pDCAe, and SCA algorithms.
result Proposed algorithms achieve high utility and sparse solutions efficiently.
Paper tackles low-rank matrix recovery with KL property and DC reformulation.
problem Low-rank matrix recovery with coarse rank estimation.
method Adds ℓ 2 , 0 \ell_{2,0} ℓ 2 , 0 -norm and balanced terms to factorized loss function; establishes KL property and DC reformulations. result Establishes KL property of exponent 1 / 2 1/2 1/2 for the composite function and its global minimizers. Solves a new bandit problem with duels and pulls for crowdsourcing.
problem Finding the best arms with mean rewards above a threshold.
method Alternates between ranking and binary search to solve TBP-DC.
result Proves optimality of the Rank-Search algorithm.
Refines pDCA_e for DC function minimization, with applications to sparse recovery and outlier detection.
problem Minimizing DC functions with specific properties.
method Refined convergence analysis of pDCA_e algorithm.
result The pDCA_e algorithm converges for level-bounded DC functions without differentiability assumptions.
Proposes an online pool generation method for DCS to improve classifier selection accuracy.
problem Difficulty in selecting competent classifiers in dynamic classifier selection techniques.
method Online local pool generation method that considers classification difficulty of samples.
result Significantly greater recognition rates compared to other pool generation methods.
pAElla detects malware in DCs/SCs with high accuracy.
problem Real-time malware detection in high-resolution data centers.
method AI-powered edge computing with IoT-based monitoring and Power Spectral Density.
result pAElla achieves F1-score close to 1 with low false alarm and malware miss rates.
Optimal withdrawal strategy for DC pension plans maximizes total withdrawals while managing risk.
problem Maximizing withdrawals from DC pension plans while managing risk.
method Optimal stochastic control approach with constraints on withdrawal and asset allocation.
result Optimal strategy yields higher average withdrawals with minimal increase in risk.