Adaptive optimization is critical in federated learning, where enabling adaptivity on both the server and client sides has proven essential for achieving optimal performance. However, the scalability of such jointly adaptive systems is often hindered by resource limitations in communication and memory. In this paper, we introduce a class of efficient adaptive algorithms, named FedAda2 and its enhanced version FedAda2++, designed specifically for large-scale, cross-device federated environments.

Conformal Prediction (CP) is a popular framework for constructing prediction bands with valid coverage in finite samples, while being free of any distributional assumption. A well-known limitation of conformal prediction is the lack of adaptivity, although several works introduced practically efficient alternate procedures. In this work, we build upon recent ideas that rely on recasting the CP problem as a statistical learning problem, directly targeting coverage and adaptivity. This statistical learning problem is based on reproducible kernel Hilbert spaces (RKHS) and kernel sum-of-squares (SoS) methods. First, we extend previous results with a general representer theorem and exhibit the dual formulation of the learning problem.

Smoothness is known to be crucial for acceleration in offline optimization, and for gradient-variation regret minimization in online learning. Interestingly, these two problems are actually closely connected -- accelerated optimization can be understood through the lens of gradient-variation online learning. In this paper, we investigate online learning with Hölder smooth functions, a general class encompassing both smooth and non-smooth (Lipschitz) functions, and explore its implications for offline optimization.

Adaptive optimization is critical in federated learning, where enabling adaptivity on both the server and client sides has proven essential for achieving optimal performance. However, the scalability of such jointly adaptive systems is often hindered by resource limitations in communication and memory. In this paper, we introduce a class of efficient adaptive algorithms, named $FedAda^2$ and its enhanced version $FedAda^2$++, designed specifically for large-scale, cross-device federated environments.

Reinforcement learning (RL) agents have demonstrated strong performance in structured environments, yet they continue to struggle in real-world settings where goals are ambiguous, conditions change dynamically, and external supervision is limited. These challenges stem not primarily from the algorithmic limitations but from the characteristics of conventional training environments, which are usually static, task-specific, and externally defined. In contrast, biological agents develop autonomy and adaptivity by interacting with complex, dynamic environments, where most behaviors are ultimately driven by internal physiological needs. Inspired by these biological constraints, we introduce EVAAA (Essential Variables in Autonomous and Adaptive Agents), a 3D virtual environment for training and evaluating egocentric RL agents endowed with internal physiological state variables. In EVAAA, agents must maintain essential variables (EVs)--e.g., satiation, hydration, body temperature, and tissue integrity (the level of damage)--within viable bounds by interacting with environments that increase in difficulty at each stage.

Effective medication management in Parkinson's Disease (PD) is challenging due to heterogeneous disease progression, variable patient response, and medication side effects. While AI models can forecast levodopa equivalent daily dose (LEDD) as a measure of medication needs, standard uncertainty quantification often fails to communicate the reliability of these predictions, treating high and low confidence clinical decisions identically. We introduce CASCADE (Calibrated Adaptive Scaling via Conformal And Distributional Estimation), a novel conformal prediction framework that propagates epistemic uncertainty from a screening classifier to adapt downstream predictions. Unlike standard conformal methods that rely on auxiliary residual regression, we leverage epistemic uncertainty from a primary classification task (identifying whether a medication change is needed) to dynamically scale the prediction intervals of a secondary regression task (predicting how much change). By mapping Venn-Abers multi-probabilistic uncertainty directly to non-conformity scores, our framework achieves continuous risk adaptation. We demonstrate that this ``cascade effect'' produces highly efficient intervals for confident patients (38.9% narrower than standard conformal baselines) while automatically expanding intervals to ensure robust coverage for uncertain cases, bridging the gap between discrete clinical decision-making and continuous dose forecasting in PD.

We compare in-context learning with fixed queries and agentic learning with adaptive queries for uniform approximation of task families. We consider two settings: an unrestricted regime, where querying and approximation are arbitrary functions, and a realizable regime, where we require these operations to be implemented by ReLU neural networks. In both settings, adaptivity never hinders approximation performance. However, this advantage can change when one passes from the unrestricted regime to the realizable regime. We identify four distinct approximation scenarios, each witnessed by an explicit task family: (a) no advantage of adaptivity; (b) an advantage in the unrestricted regime that persists under ReLU realizability; (c) an advantage that arises only under realizability; and (d) an advantage that disappears under realizability. This demonstrates that representational constraints interact profoundly with the effect of adaptivity.

A.1 Face experiments For the encoder, we use a resnet-50 backbone followed by projection heads that output pointwise, lower and upper quantile predictions. Each projection head consists of a convolution layer followed by a Leaky-Relu activation and a global average pooling layer. The input to each projection head is the output of the backbone network - a feature map of size 512 4 4 and the output dimension is the number of style dimensions - in the case of the pretrained FFHQ styleGAN2 used in our experiments, this value is 9088. For the generator, we use a FFHQ pretrained styleGAN2 trained to output faces of resolution 1024 1024 obtained from the official implementation. No discriminator is used during training.