15 problems

Stochastic exp-concave optimization (SXO) concerns minimizing the population objective from stochastic gradient-oracle queries in dimension $d$, to accuracy $\epsilon$. Optimal-run…

Consider deterministic strongly convex optimization, where an algorithm is called universal if it achieves the relevant near-optimal convergence rates without prior knowledge of pr…

The stochastic online feedback optimization framework considers agents that may be non-compliant with commands issued by a central controller or multiple local controllers. In the…

Optimality conjecture. When $c=\gamma=1$, the coefficient $\gamma^2/(1+c\gamma^2)$ is optimal; equivalently, no higher approximation coefficient is possible for the corresponding o…

The framework uses exponentially increasing weights, corresponding to a constant $c_t=\gamma$, and these weights achieve optimal worst-case convergence guarantees. Instance-depende…

Arithmetic-complexity conjecture. Without additional assumptions on the data-generating distribution, it is not possible to find an $varepsilon$-optimal point using fewer than…

PID controllers are studied under a real-roots assumption on the transfer function, while the experiments include parameter choices that do not satisfy this assumption and neverthe…

The analysis considers PID controllers whose transfer function has real roots, corresponding to an overdamped linear filter; imaginary roots instead correspond to an underdamped os…

Let $\Theta\subseteq\mathbf{R}^d$ be the constraint set in stochastic or online convex optimization, and define its coordinatewise square by … Call $\Theta$ quadratically convex wh…

The setting is online linear-quadratic tracking with prediction window $W$, horizon $N$, variation budget $L_N$, and condition number $\zeta$; the regret bounds above differ by a s…

The algorithms considered use different amounts of information about the hitting-cost function: OBD PLUS uses projection onto different level sets, Weighted Greedy queries gradient…

Let an any-time algorithm be an SGD algorithm that does not require a priori knowledge of the total number of iterations $T$. Let $G$ be the gradient bound and $D$ the diameter par…

In online convex optimization, data points arrive in streams and the probabilistic model generating them may change over time, so the optimal point $x^{*,t}$ moves during the optim…

In decentralized online optimization, suppose that agents receive multiple gradients during each time step. Multiple-gradient conjecture. Our theoretical results can be strengthene…

Assume that, at each time $t$, Assumption (A4) provides an exact computational oracle for the maximizer ${\hat{\mathbf{x}}}_t$, and that Assumption (A3) imposes concavity of the fu…