In federated language modeling, $K$ nodes each hold $n$ samples but cannot pool data or exchange full-precision gradients or weights. We study the minimax rate at which a conditional distribution over $V$ tokens can be estimated when each node may upload at most $B$ bits per query in a public probe set. In federated probe-logit distillation (FPLD), each node transmits a scalar-quantized logit vector on the probe set, and an aggregator distills a global parametric student. Prior work (Dubey and Huo, 2026) establishes a high-probability KL rate $O(d/(Kn) + ρ\sqrt{V \log V / m} + K^{-1} \cdot 2^{-2B/V})$ plus optimization slack, with the bandwidth term in its trace-sharpened form. Whether this bandwidth-term rate is tight, and how the upper bound generalizes to heterogeneous per-node bandwidths, are left open. We close both gaps. First, the dithered FPLD construction has a matching single-round lower bound $Ω(K^{-1} \cdot 2^{-2B/V})$ under non-degeneracy, pinning the bandwidth-axis rate at $Θ(K^{-1} \cdot 2^{-2B/V})$. $T$-round sequential refinement with nested/scaled residual quantizers achieves $O(K^{-1} \cdot 2^{-2TB/V})$; vanilla FPLD's $T$-independent bandwidth term is suboptimal for every $T > 1$. Second, we establish a heterogeneous-bandwidth upper bound for per-node budgets $B_i$, paired with a closed-form optimal allocation $B_i^* = B_{\mathrm{tot}}/K + (V/2) \log_2(w_i / \bar{w}_g)$, a log-tilted water-filling rule that is the per-node analogue of reverse water-filling for distortion-rate optimization. A plug-in adaptive variant estimates the weights from a short warm-up phase and attains $1 + O(\sqrt{\log(K/δ)/(m T_0)})$ relative suboptimality. Synthetic n-gram simulations confirm that empirical KL is bracketed by the upper and lower bounds and that the optimal allocation strictly dominates uniform and inverse-weighted baselines under heterogeneous clipping.

We study the fixed-budget max-min action identification problem in depth-2 max-min trees, an important special case of Monte Carlo Tree Search. A learner sequentially allocates $T$ samples to leaves and then recommends a subtree whose minimum leaf value is largest. Motivated by approximate planning, we focus on $\varepsilon$-good subtree identification, where any subtree whose min value is within $\varepsilon$ of the optimal maximin value is acceptable. Our main contribution is an $\varepsilon$-agnostic algorithm: it does not require $\varepsilon$ as input, but achieves instance-dependent error bounds for every meaningful $\varepsilon$. We show that the misidentification probability decays as $\exp(-\widetildeΘ(T/H_2(\varepsilon)))$, where $H_2(\varepsilon)$ captures both cross-subtree and within-subtree gaps. When each subtree has a single leaf, the problem reduces to standard fixed-budget best-arm identification, and our analysis recovers, up to accelerating factors, known $\varepsilon$-good guarantees for halving-style methods while giving a new $\varepsilon$-good guarantee for Successive Rejects. On the lower-bound side, we provide complementary positive and negative results showing that max-min identification has a different hardness structure from standard $K$-armed bandits. To our knowledge, this is the first provable fixed-budget algorithmic guarantee for max-min action identification.

This paper presents IB-POMCP, a novel algorithm for online planning under partial observability. Our approach enhances the decision-making process by using estimations of the world belief's entropy to guide a tree search process and surpass the limitations of planning in scenarios with sparse reward configurations. By performing what we denominate as an information-guided planning process, the algorithm, which incorporates a novel I-UCB function, shows significant improvements in reward and reasoning time compared to state-of-the-art baselines in several benchmark scenarios, along with theoretical convergence guarantees.

Table 2, Table 3, and Table 4 provide top-1 action, top-5 action, and winner accuracies, respectively, between each headset in the neural network. Figure 1 shows game length distributions for each headset. The synopsis features were hand-designed. Many of them are natural given the rules of chess. Some of them are near duplicates of each other.

In this work, we address risk-averse Bayes-adaptive reinforcement learning. We pose the problem of optimising the conditional value at risk (CVaR) of the total return in Bayes-adaptive Markov decision processes (MDPs). We show that a policy optimising CVaR in this setting is risk-averse to both the epistemic uncertainty due to the prior distribution over MDPs, and the aleatoric uncertainty due to the inherent stochasticity of MDPs. We reformulate the problem as a two-player stochastic game and propose an approximate algorithm based on Monte Carlo tree search and Bayesian optimisation. Our experiments demonstrate that our approach significantly outperforms baseline approaches for this problem.

You are a robot and you live in a Markov decision process (MDP) with a finite or an infinite number of transitions from state-action to next states. You got brains and so you plan before you act. Luckily, your roboparents equipped you with a generative model to do some Monte-Carlo planning. The world is waiting for you and you have no time to waste. You want your planning to be efficient.