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Key research themes
1. How can online convex optimization algorithms leverage noisy or imperfect predictions for efficient parameter estimation?
This research theme investigates the design and analysis of online convex optimization (OCO) algorithms that exploit noisy predictions about future costs or parameters to improve decision-making in sequential settings. It is crucial because practical systems often operate with imperfect forecasts, and effectively integrating prediction uncertainty can lead to algorithms that balance adaptation and robustness, minimize regret, and provide strong performance guarantees even with switching costs.
Key finding: Introduces a novel class of Committed Horizon Control (CHC) policies, generalizing Receding Horizon Control (RHC) and Averaging Fixed Horizon Control (AFHC), for OCO with switching costs and noisy predictions. Provides... Read more
Key finding: Develops a stochastic prediction error model including error correlations and improving forecasts over time, extending prior work in machine learning and control communities. Demonstrates that sublinear regret and constant... Read more
Key finding: Provides a rigorous foundational framework situating online convex optimization as a learning process that adapts decisions iteratively with exposure to new cost functions, embracing noisy or incomplete predictive... Read more
2. What methods enable robust online parameter estimation in nonlinear and dynamical systems using combined filtering and optimization techniques?
This theme focuses on algorithms and frameworks that estimate parameters online in nonlinear continuous- and discrete-time dynamical systems with uncertainties, via filtering frameworks integrating particle and Kalman filters or adaptive observers. It addresses statistical challenges like parameter degeneracy, computational complexity, and non-convexity, with applications to state-space models in engineering, control systems, and time-series forecasting. Achieving efficient estimators ensures accurate, adaptive models for real-time decision-making in complex environments.
Key finding: Proposes a semi-recursive two-layer algorithm combining particle filtering for static parameter posterior estimation in the outer layer with Kalman filtering for state estimation in the inner layer. Introduces a dynamic... Read more
Key finding: Presents an online stochastic estimator for continuous-time second order Wiener systems using differential mean-value theorem and stochastic contraction theory. Proves boundedness and asymptotic convergence of parameter and... Read more
Key finding: Introduces an adaptive Particle Swarm Optimization (PSO) algorithm with adaptive inertia weighting to balance exploration-exploitation, enhancing convergence speed and accuracy for bilinear system parameter estimation. Also... Read more
Key finding: Elaborates on the adaptive PSO framework for bilinear system parameters, detailing performance improvements in accuracy and computational efficiency over classical recursive and heuristic identification methods. Demonstrates... Read more
3. How can online learning frameworks be structured to efficiently handle complex structured loss spaces and model selection procedures in time-evolving environments?
This theme examines online learning algorithms designed for structured prediction problems where losses and model components exhibit special geometric or combinatorial structures such as sparsity, low-rankness, or additive combinations thereof, as well as dynamically adapting model selection mechanisms for sequential prediction. These frameworks aim to improve regret guarantees by exploiting structure or by dynamically choosing the best model selection procedure (MSP), balancing bias-variance trade-offs and computational efficiency in nonstationary environments.
Key finding: Develops a general online mirror descent (OMD) algorithm for prediction with expert advice where loss vectors lie in a Minkowski sum of atomic norm balls, allowing exploitation of structure such as noisy low-rank or sparse... Read more
Key finding: Proposes a flexible online prediction technique that dynamically chooses among multiple model selection procedures (MSPs) over time, leveraging the insight that each MSP is optimal for specific model classes. The approach... Read more
Key finding: Introduces a kernel-based online prediction algorithm that integrates sparsification techniques and covariance matrix adaptation evolution strategy (CMA-ES) optimization of general symmetric kernel covariance matrices.... Read more