We study the problem of active pure exploration with fixed confidence in generic stochastic bandit environments. The goal of the learner is to answer a query about the environment with a given level of certainty while minimizing her sampling budget. For this problem, instance-specific lower bounds on the expected sample complexity reveal the optimal proportions of arm draws an Oracle algorithm would apply. These proportions solve an optimization problem whose tractability strongly depends on the structural properties of the environment, but may be instrumental in the design of efficient learning algorithms. We devise Frank-Wolfe-based Sampling (FWS), a simple algorithm whose sample complexity matches the lower bounds for a wide class of pure exploration problems. The algorithm is computationally efficient as, to learn and track the optimal proportion of arm draws, it relies on a single iteration of Frank-Wolfe algorithm applied to the lower-bound optimization problem. We apply FWS to various pure exploration tasks, including best arm identification in unstructured, thresholded, linear, and Lipschitz bandits. Despite its simplicity, FWSis competitive compared to state-of-art algorithms.

We study fixed-confidence Best Arm Identification (BAI) in semiparametric bandits, where rewards are linear in arm features plus an unknown additive baseline shift. Unlike linear-bandit BAI, this setting requires orthogonalized regression, and its instance-optimal sample complexity has remained open. For the transductive setting, we establish an attainable instance-dependent lower bound characterized by the corresponding linear-bandit complexity on shifted features. We then propose a computationally efficient phase-elimination algorithm based on a new $XY$-design for orthogonalized regression. Our analysis yields a nearly optimal high-probability sample-complexity upper bound, up to log factors and an additive $d^2$ term, and experiments on synthetic instances and the Jester dataset show clear gains over prior baselines.

The agent pulls an arm and observes the corresponding return provided by the environment.

The agent pulls an arm and observes the corresponding return provided by the environment.

The development of alignment and reasoning capabilities in large language models has seen remarkable progress through two paradigms: instruction tuning and reinforcement learning from human feedback (RLHF) alignment paradigm, and distillation-based reasoning fine-tuning paradigm. While both approaches prove effective independently, the third paradigm of applying RLHF to distillation-trained models presents significant challenges. Our investigation reveals two critical phenomena that emerge in this paradigm: Sequence Length Collapse, where language generation dramatically reduces during early RLHF training, and the Reward Hockey Stick Curve, featuring severe reward score drops followed by gradual recovery. These instabilities fundamentally compromise the model's alignment and reasoning capabilities. To address these challenges, we propose Balanced Actor Initialization (BAI), a two-stage weighted model merging approach. BAI first merges instruction-following and distillation-based reasoning fine-tuned models, then further combines this intermediate model with the pretrained model to preserve foundational knowledge. Through comprehensive experiments across diverse benchmarks and detailed analysis of training experiments, we demonstrate that BAI resolves Sequence Length Collapse, mitigates the Reward Hockey Stick Curve, and enables continuous sequence length improvement during training. Additionally, our analysis reveals that balanced merging ratios achieve optimal trade-offs between training stability and reasoning capability preservation. Our work provides the effective solution for stable training in this third paradigm, enabling more capable reasoning models that combine distillation efficiency with RLHF alignment.

We propose a {\em novel} piecewise stationary linear bandit (PSLB) model, where the environment randomly samples a context from an unknown probability distribution at each changepoint, and the quality of an arm is measured by its return averaged over all contexts. The contexts and their distribution, as well as the changepoints are unknown to the agent. We design {\em Piecewise-Stationary $\varepsilon$-Best Arm Identification$^+$} (PS$\varepsilon$BAI$^+$), an algorithm that is guaranteed to identify an $\varepsilon$-optimal arm with probability $\ge 1-\delta$ and with a minimal number of samples. PS$\varepsilon$BAI$^+$ consists of two subroutines, PS$\varepsilon$BAI and {\sc Na\"ive $\varepsilon$-BAI} (N$\varepsilon$BAI), which are executed in parallel. PS$\varepsilon$BAI actively detects changepoints and aligns contexts to facilitate the arm identification process. When PS$\varepsilon$BAI and N$\varepsilon$BAI are utilized judiciously in parallel, PS$\varepsilon$BAI$^+$ is shown to have a finite expected sample complexity. By proving a lower bound, we show the expected sample complexity of PS$\varepsilon$BAI$^+$ is optimal up to a logarithmic factor. We compare PS$\varepsilon$BAI$^+$ to baseline algorithms using numerical experiments which demonstrate its efficiency. Both our analytical and numerical results corroborate that the efficacy of PS$\varepsilon$BAI$^+$ is due to the delicate change detection and context alignment procedures embedded in PS$\varepsilon$BAI.

Motivated by real-world applications that necessitate responsible experimentation, we introduce the problem of best arm identification (BAI) with minimal regret. This innovative variant of the multi-armed bandit problem elegantly amalgamates two of its most ubiquitous objectives: regret minimization and BAI. More precisely, the agent's goal is to identify the best arm with a prescribed confidence level $\delta$, while minimizing the cumulative regret up to the stopping time. Focusing on single-parameter exponential families of distributions, we leverage information-theoretic techniques to establish an instance-dependent lower bound on the expected cumulative regret. Moreover, we present an intriguing impossibility result that underscores the tension between cumulative regret and sample complexity in fixed-confidence BAI. Complementarily, we design and analyze the Double KL-UCB algorithm, which achieves asymptotic optimality as the confidence level tends to zero. Notably, this algorithm employs two distinct confidence bounds to guide arm selection in a randomized manner. Our findings elucidate a fresh perspective on the inherent connections between regret minimization and BAI.

Autoregressive Sequence-To-Sequence models are the foundation of many Deep Learning achievements in major research fields such as Vision and Natural Language Processing. Despite that, they still present significant limitations. For instance, when errors occur in the early steps of the prediction, the whole output is severely affected. Such reliance on previously predicted tokens and the inherent computational unfriendliness of sequential algorithms, motivated researchers to explore different architectures and methods in the search for bidirectional approaches. In this work, we introduce the Bidirectional Awareness Induction (BAI), a training method that leverages a subset of elements in the network, the Pivots, to perform bidirectional learning without breaking the autoregressive constraints. To showcase its flexibility, we apply the method to three architectures, the Transformer, ExpansionNet v2 and GPT, then perform experiments over three tasks. Experimental results showcase BAI's effectiveness on all selected tasks and architectures. In particular, we observed an increase of up to 2.4 CIDEr in Image-Captioning, 4.96 BLEU in Neural Machine Translation, and 1.16 ROUGE in Text Summarization compared to the respective baselines. Notably, BAI not only has a positive impact on models trained from scratch but on pre-trained models as well. Such an aspect, combined with the absence of architectural requirements synergizes well with the current trend of LLMs.

We study the stochastic multi-armed bandit problem in the $P$-pass streaming model. In this problem, the $n$ arms are present in a stream and at most $m