Vasilis Pollatos

Anas Barakat, Andreas Kontogiannis, Vasilis Pollatos et al.

We study adversarial online learning with hidden-convex losses, i.e., nonconvex losses that become convex after a nonlinear reparameterization. Ghai, Lu and Hazan (2022) proved that, under geometric and smoothness assumptions, online gradient descent (OGD) on such nonconvex losses approximately simulates online mirror descent (OMD) on the underlying convex losses with a suitable regularizer, yielding $\mathcal{O}(T^{2/3})$ regret. They left open whether the optimal $Θ(\sqrt{T})$ regret from online convex optimization can be recovered in this hidden-convex setting. We answer this question affirmatively. More specifically, via a sharper discrete-time algorithmic equivalence argument, we prove that OGD achieves $\mathcal{O}(\sqrt{T})$ regret under the same assumptions, matching the optimal worst-case rate for adversarial online convex optimization. We also address another open question of Ghai, Lu and Hazan (2022) by clarifying the geometry required for this algorithmic equivalence. We replace the diagonal-Jacobian sufficient condition with a necessary-and-sufficient Hessian compatibility condition, thereby expanding the class of admissible reparameterizations. We complement our tight regret bound with a lower bound showing that the Hessian compatibility assumption is essential for OGD; when it fails, we construct a smooth reparameterization and an adversarial sequence of hidden-convex losses for which OGD suffers $Ω(T)$ regret. Finally, we extend our analysis to one-point bandit feedback and prove a $\mathcal{O}(T^{3/4})$ expected regret bound for bandit OGD with spherical smoothing, matching its classical rate on convex losses.

Andreas Kontogiannis, Vasilis Pollatos, Panayotis Mertikopoulos et al.

This paper addresses the problem of designing efficient no-swap regret algorithms for combinatorial bandits, where the number of actions $N$ is exponentially large in the dimensionality of the problem. In this setting, designing efficient no-swap regret translates to sublinear -- in horizon $T$ -- swap regret with polylogarithmic dependence on $N$. In contrast to the weaker notion of external regret minimization - a problem which is fairly well understood in the literature - achieving no-swap regret with a polylogarithmic dependence on $N$ has remained elusive in combinatorial bandits. Our paper resolves this challenge, by introducing a no-swap-regret learning algorithm with regret that scales polylogarithmically in $N$ and is tight for the class of combinatorial bandits. To ground our results, we also demonstrate how to implement the proposed algorithm efficiently -- that is, with a per-iteration complexity that also scales polylogarithmically in $N$ -- across a wide range of well-studied applications.

Vasilis Pollatos, Debmalya Mandal, Goran Radanovic

In performative Reinforcement Learning (RL), an agent faces a policy-dependent environment: the reward and transition functions depend on the agent's policy. Prior work on performative RL has studied the convergence of repeated retraining approaches to a performatively stable policy. In the finite sample regime, these approaches repeatedly solve for a saddle point of a convex-concave objective, which estimates the Lagrangian of a regularized version of the reinforcement learning problem. In this paper, we aim to extend such repeated retraining approaches, enabling them to operate under corrupted data. More specifically, we consider Huber's $ε$-contamination model, where an $ε$ fraction of data points is corrupted by arbitrary adversarial noise. We propose a repeated retraining approach based on convex-concave optimization under corrupted gradients and a novel problem-specific robust mean estimator for the gradients. We prove that our approach exhibits last-iterate convergence to an approximately stable policy, with the approximation error linear in $\sqrtε$. We experimentally demonstrate the importance of accounting for corruption in performative RL.

Andreas Kontogiannis, Ioannis Panageas, Vasilis Pollatos

While first-order stationary points (FOSPs) are the traditional targets of non-convex optimization, they often correspond to undesirable strict saddle points. To circumvent this, attention has shifted towards second-order stationary points (SOSPs). In unconstrained settings, finding approximate SOSPs is PLS-complete (Kontogiannis et al.), matching the complexity of finding unconstrained FOSPs (Hollender and Zampetakis). However, the complexity of finding SOSPs in constrained settings remained notoriously unclear and was highlighted as an important open question by both aforementioned works. Under one strict definition, even verifying whether a point is an approximate SOSP is NP-hard (Murty and Kabadi). Under another widely adopted, relaxed definition where non-negative curvature is required only along the null space of the active constraints, the problem lies in TFNP, and algorithms with O(poly(1/epsilon)) running times have been proposed (Lu et al.). In this work, we settle the complexity of constrained SOSP by proving that computing an epsilon-approximate SOSP under the tractable definition is PLS-complete. We demonstrate that our result holds even in the 2D unit square [0,1]^2, and remarkably, even when stationary points are isolated at a distance of Omega(1) from the domain's boundary. Our result establishes a fundamental barrier: unless PLS is a subset of PPAD (implying PLS = CLS), no deterministic, iterative algorithm with an efficient, continuous update rule can exist for finding approximate SOSPs. This contrasts with the constrained first-order counterpart, for which Fearnley et al. showed that finding an approximate KKT point is CLS-complete. Finally, our result yields the first problem defined in a compact domain to be shown PLS-complete beyond the canonical Real-LocalOpt (Daskalakis and Papadimitriou)."

Andreas Kontogiannis, Dimitrios Kelesis, Vasilis Pollatos et al.

A focused crawler aims at discovering as many web pages and web sites relevant to a target topic as possible, while avoiding irrelevant ones. Reinforcement Learning (RL) has been a promising direction for optimizing focused crawling, because RL can naturally optimize the long-term profit of discovering relevant web locations within the context of a reward. In this paper, we propose TRES, a novel RL-empowered framework for focused crawling that aims at maximizing both the number of relevant web pages (aka \textit{harvest rate}) and the number of relevant web sites (\textit{domains}). We model the focused crawling problem as a novel Markov Decision Process (MDP), which the RL agent aims to solve by determining an optimal crawling strategy. To overcome the computational infeasibility of exhaustively searching for the best action at each time step, we propose Tree-Frontier, a provably efficient tree-based sampling algorithm that adaptively discretizes the large state and action spaces and evaluates only a few representative actions. Experimentally, utilizing online real-world data, we show that TRES significantly outperforms and Pareto-dominates state-of-the-art methods in terms of harvest rate and the number of retrieved relevant domains, while it provably reduces by orders of magnitude the number of URLs needed to be evaluated at each crawling step.

Vasilis Pollatos, Loukas Kouvaras, Eleni Charou

In this paper we present our work on developing an automated system for land cover classification. This system takes a multiband satellite image of an area as input and outputs the land cover map of the area at the same resolution as the input. For this purpose convolutional machine learning models were trained in the task of predicting the land cover semantic segmentation of satellite images. This is a case of supervised learning. The land cover label data were taken from the CORINE Land Cover inventory and the satellite images were taken from the Copernicus hub. As for the model, U-Net architecture variations were applied. Our area of interest are the Ionian islands (Greece). We created a dataset from scratch covering this particular area. In addition, transfer learning from the BigEarthNet dataset [1] was performed. In [1] simple classification of satellite images into the classes of CLC is performed but not segmentation as we do. However, their models have been trained into a dataset much bigger than ours, so we applied transfer learning using their pretrained models as the first part of out network, utilizing the ability these networks have developed to extract useful features from the satellite images (we transferred a pretrained ResNet50 into a U-Res-Net). Apart from transfer learning other techniques were applied in order to overcome the limitations set by the small size of our area of interest. We used data augmentation (cutting images into overlapping patches, applying random transformations such as rotations and flips) and cross validation. The results are tested on the 3 CLC class hierarchy levels and a comparative study is made on the results of different approaches.