Proposes SOR Q-learning for faster optimal value function computation in RL.
problem Finding optimal value function in Markov Decision Processes (MDPs).
method Successive Over-Relaxation (SOR) applied to Q-learning algorithm.
result SOR Q-learning converges faster to optimal value function compared to standard Q-learning.
Proposes a faster second-order method for MDPs.
problem Slow convergence of first-order value iteration methods in MDPs.
method Applies Newton-Raphson method to successive relaxation value iteration scheme.
result Second-order convergence and faster convergence to optimal solution.
Framework for incomplete multi-view learning improves efficiency and clustering accuracy.
problem Incomplete representation in multi-view data.
method Joint Embedding Learning and Low-Rank Approximation (JELLA) framework.
result Improves efficiency and clustering accuracy in incomplete multi-view data.
The framework of Integral Quadratic Constraints (IQC) reduces the computation of upper bounds on the convergence rate of several optimization algorithms to a semi-definite program (SDP). In the case of over-relaxed Alternating Direction Method of Multipliers (ADMM), an explicit and closed form solution to this SDP was …
This paper studies the optimal VIX futures trading problems under a regime-switching model. We consider the VIX as mean reversion dynamics with dependence on the regime that switches among a finite number of states. For the trading strategies, we analyze the timings and sequences of the investor's market participation,…
The framework of Integral Quadratic Constraints of Lessard et al. (2014) reduces the computation of upper bounds on the convergence rate of several optimization algorithms to semi-definite programming (SDP). Followup work by Nishihara et al. (2015) applies this technique to the entire family of over-relaxed Alternating…
In this paper we present qualitative and quantitative comparison of various analytical and numerical approximation methods for calculating a position of the early exercise boundary of the American put option paying zero dividends. First we analyze their asymptotic behavior close to expiration. In the second part of the…
Statistical image reconstruction (SIR) methods are studied extensively for X-ray computed tomography (CT) due to the potential of acquiring CT scans with reduced X-ray dose while maintaining image quality. However, the longer reconstruction time of SIR methods hinders their use in X-ray CT in practice. To accelerate st…
This paper deals with pricing of European and American options, when the underlying asset price follows Heston model, via the interior penalty discontinuous Galerkin finite element method (dGFEM). The advantages of dGFEM space discretization with Rannacher smoothing as time integrator with nonsmooth initial and boundar…
We propose and analyze a constrained level-set method for semi-automatic image segmentation. Our level-set model with constraints on the level-set function enables us to specify which parts of the image lie inside respectively outside the segmented objects. Such a-priori information can be expressed in terms of upper a…
In this paper we investigate a nonlinear generalization of the Black-Scholes equation for pricing American style call options in which the volatility term may depend on the underlying asset price and the Gamma of the option. We propose a numerical method for pricing American style call options by means of transformatio…
A learning algorithm optimizes SOR solver parameters for a sequence of linear systems efficiently.
problem Optimizing solver parameters for a sequence of related linear systems without extra computations.
method Bandit and contextual bandit algorithms for online learning of optimal parameters.
result The overall cost approaches the best fixed parameter as the sequence length increases.
Chebyshev steps improve convergence in deep-unfolded gradient descent.
problem Improving convergence speed in iterative algorithms.
method Introducing Chebyshev steps to bound convergence rate of gradient descent.
result Chebyshev steps lead to asymptotically optimal convergence rate.
New algorithm improves tensor completion performance.
problem Tensor completion for partially observed data.
method Adaptive ADMM optimization framework for low-rank tensor completion.
result New method outperforms conventional techniques in NMSE.
When solving consensus optimization problems over a graph, there is often an explicit characterization of the convergence rate of Gradient Descent (GD) using the spectrum of the graph Laplacian. The same type of problems under the Alternating Direction Method of Multipliers (ADMM) are, however, poorly understood. For i…
Success conditioning optimizes policies by imitating successful trajectories, solving a trust-region optimization problem.
problem Improving policies through random actions that lead to desired outcomes.
method Success conditioning, which involves collecting and updating policies based on successful trajectories.
result Success conditioning solves a trust-region optimization problem, maximizing policy improvement with a χ2 divergence constraint. Paper proposes a new method for training nonconvex models.
problem Training nonconvex models like neural networks.
method Successive functional gradient optimization using mirror descent in a function space.
result The method leads to better performance than standard training techniques.
Paper tackles non-convex optimization for higher moments in portfolio management.
problem Complexity of higher moments in optimization problems.
method Method of successive convex approximation.
result Solves mean-variance-skewness problem using non-convex optimization.
GRPO optimizes LLMs with verifiable rewards, amplifying policy success.
problem Improving LLMs' reasoning under verifiable binary rewards.
method Introduces GRPO, analyzes variants of reward normalization and regularization.
result GRPO amplifies policy success, converging to a fixed point exceeding the reference.
Study improves efficiency of MIMO systems' sum rate estimation.
problem Maximizing sum rate in MIMO systems with PAPC constraints.
method Proposes two new low-complexity approaches: alternating optimization and machine learning.
result Demonstrates superior performance compared to existing methods.
The paper introduces SuccessProbaMax to optimize policy success probability in online advertising.
problem Optimizing policy success probability in online advertising systems.
method SuccessProbaMax algorithm that optimizes for the probability of success rather than expected value.
result SuccessProbaMax outperforms conventional algorithms in terms of success rate.
Study on information evolution in interactive decision making using multi-armed bandits.
problem Understanding information dynamics in interactive decision making.
method Stochastic multi-armed bandit problem, focusing on optimal arm with a fixed margin.
result Distinct growth phases in mutual information, showing decoupling between success probability and information gain.
This work explains GANs as Bayesian neural networks with partial stochasticity.
problem Challenges in optimizing GANs and understanding their limitations.
method Interpreting GANs as Bayesian neural networks with partial stochasticity, establishing conditions, and proposing strategies to smooth the loss landscape and find solutions with minimum description length.
result Proposed strategies lead to performance improvements and deeper understanding of GANs.
Integrates ESG data into Black-Litterman for portfolio optimization.
problem Optimizing portfolios with ESG considerations.
method Black-Litterman framework with Stein shrinkage for ESG bias, multivariate affine normal-inverse Gaussian model, CVaR risk measure, daily reallocation.
result Successful portfolio optimization with returns of 40-45% annually.
New algorithms optimize multiple machine learning metrics in real-world tasks.
problem Optimizing multiple conflicting performance criteria in real-world applications.
method Extends ASHA to multi-objective hyperparameter optimization.
result MO ASHA enables scalable multi-objective hyperparameter optimization.
Graph neural networks improve solving linear optimization problems.
problem Improving the efficiency of solving linear optimization problems.
method Using graph neural networks to simulate standard interior-point methods for linear optimization problems.
result Graph neural networks can solve linear optimization problems close to optimality, often outperforming conventional solvers.
GAIL with neural networks converges to global optima and has a known rate.
problem Uncertainty about GAIL with neural networks achieving global optimality.
method Gradient-based alternating updates algorithm.
result Established sublinear convergence to globally optimal solution.
Paper proposes a new tensor imputation method for spatiotemporal traffic data with missing patterns.
problem Imputation of corrupted or incomplete traffic data.
method Truncated tensor Schatten p-norm (TSpN) for spatiotemporal traffic data imputation.
result The proposed method outperforms other state-of-the-art tensor-based imputation models in various missing cases.
Optimizes non-linear outcomes from summed contributions.
problem Maximizing a non-linear function of summed small contributions.
method Derives a scalable descent algorithm leveraging concentration properties.
result Directly optimizes for stated objective, e.g., A/B test success criterion.
Investment strategy optimized in markets with transaction costs and search delays.
problem Maximizing wealth in an illiquid market with transaction costs and search frictions.
method Characterized no-trade region and provided asymptotic expansions of value function for small transaction costs.
result The effects of transaction costs are more pronounced in illiquid markets.
MeRL learns from sparse, underspecified rewards by discounting spurious trajectories.
problem Learning from binary success-failure feedback with little context.
method MeRL uses KL divergence to collect diverse successful trajectories and optimize an auxiliary reward function.
result MeRL outperforms alternative reward learning techniques and achieves state-of-the-art performance.
The paper tackles best arm identification in contaminated bandits with optimal error guarantees and sample complexity.
problem Best arm identification in stochastic bandits with adversarial reward contamination.
method Proposes two algorithms: a gap-based algorithm and a successive elimination-based algorithm for sub-Gaussian bandits.
result Asymptotically optimal sample complexity for both algorithms.
This thesis explores optimization methods for high-dimensional machine learning problems.
problem High-dimensional optimization challenges in machine learning.
method Intuition and convergence proofs for stochastic gradient descent and momentum methods.
result Explanation of why common machine learning optimization methods are successful.
A new private algorithm for bandit problems meets lower bounds.
problem Optimal private solution for stochastic multi-arm bandit.
method Private Successive Elimination based on optimal private stopping rule.
result Optimal private algorithm meets both non-private and private lower bounds.
This paper studies a class of optimal multiple stopping problems driven by Lévy processes. Our model allows for a negative effective discount rate, which arises in a number of financial applications, including stock loans and real options, where the strike price can potentially grow at a higher rate than the original d…
The muti-layer information bottleneck (IB) problem, where information is propagated (or successively refined) from layer to layer, is considered. Based on information forwarded by the preceding layer, each stage of the network is required to preserve a certain level of relevance with regards to a specific hidden variab…
Bayesian optimization has become a successful tool for hyperparameter optimization of machine learning algorithms, such as support vector machines or deep neural networks. Despite its success, for large datasets, training and validating a single configuration often takes hours, days, or even weeks, which limits the ach…
The paper defines successful active management and introduces a framework.
problem The elusive criteria for successful active management in the literature.
method Introducing definitions of key concepts and a logically coherent evaluation framework.
result A strong defense of active management emerges through the defined concepts.
To maximize its success, an AGI typically needs to explore its initially unknown world. Is there an optimal way of doing so? Here we derive an affirmative answer for a broad class of environments.
Momentum Stochastic Gradient Descent (MSGD) algorithm has been widely applied to many nonconvex optimization problems in machine learning, e.g., training deep neural networks, variational Bayesian inference, and etc. Despite its empirical success, there is still a lack of theoretical understanding of convergence proper…
Generative Adversarial Networks (GANs) have achieved remarkable results in the task of generating realistic natural images. In most successful applications, GAN models share two common aspects: solving a challenging saddle point optimization problem, interpreted as an adversarial game between a generator and a discrimi…
PASOA optimizes Bayesian design by improving SMC samplers and EIG.
problem Sequential design optimization for accurate parameter inference.
method Sequential optimization using contrastive estimation, SMC samplers, and tempering.
result PASOA optimizes design and inference with improved consistency.
New bandit problem for finding best group of arms with worst mean reward.
problem Finding the best group of arms with the worst mean reward in overlapping groups.
method Two algorithms based on successive elimination and robust optimization.
result Upper bounds on the number of samples to find max-min optimal or near-optimal group.
Dan Lovallo and Daniel Kahneman must be commended for their clear identification of causes and cures to the planning fallacy in "Delusions of Success: How Optimism Undermines Executives' Decisions" (HBR July 2003). Their look at overoptimism, anchoring, competitor neglect, and the outside view in forecasting is highly …
Paper proposes a new Hessian-aware zeroth-order optimization for improving black-box adversarial attacks.
problem Improving black-box adversarial attacks on neural networks.
method Introduces a Hessian-aware zeroth-order optimization algorithm called ZO-HessAware.
result ZO-HessAware achieves improved success rates with lower query complexity.
Vanguard uses AI to create personalized financial plans.
problem Challenges in choosing features for complex financial planning.
method Reinforcement learning for identifying optimal savings rates.
result Trains algorithms to model financial success trajectories.
Bayesian optimization outperforms other methods in hyperparameter tuning for reinforcement learning.
problem Finding optimal hyperparameters that generalize across random seeds in reinforcement learning.
method Benchmarked Successive Halving, Random Search, and Bayesian Optimization with and without repetitions on PPO2 algorithms for Cartpole and Inverted Pendulum tasks.
result Bayesian optimization with noise robust acquisition function is the best choice.
Distillation speeds up classifier training and provides insights into its success.
problem Empirical success of knowledge distillation without theoretical explanation.
method Study of linear and deep linear classifiers, proving a generalization bound.
result Three key factors for distillation success: data geometry, optimization bias, strong monotonicity.