Monte-Carlo Tree Search (MCTS) methods, such as Upper Confidence Bound applied to Trees (UCT), are instrumental to automated planning techniques. However, UCT can be slow to explore an optimal action when it initially appears inferior to other actions. Maximum ENtropy Tree-Search (MENTS) incorporates the maximum entropy principle into an MCTS approach, utilising Boltzmann policies to sample actions, naturally encouraging more exploration. In this paper, we highlight a major limitation of MENTS: optimal actions for the maximum entropy objective do not necessarily correspond to optimal actions for the original objective. We introduce two algorithms, Boltzmann Tree Search (BTS) and Decaying ENtropy Tree-Search (DENTS), that address these limitations and preserve the benefits of Boltzmann policies, such as allowing actions to be sampled faster by using the Alias method. Our empirical analysis shows that our algorithms show consistent high performance across several benchmark domains, including the game of Go.

Despite its widespread use, there is virtually no theoretical understanding about the limitations or the actual benefits of this exploration scheme.

5G networks enable diverse services such as eMBB, URLLC, and mMTC through network slicing, necessitating intelligent admission control and resource allocation to meet stringent QoS requirements while maximizing Network Service Provider (NSP) profits. However, existing Deep Reinforcement Learning (DRL) frameworks focus primarily on profit optimization without explicitly accounting for service delay, potentially leading to QoS violations for latency-sensitive slices. Moreover, commonly used epsilon-greedy exploration of DRL often results in unstable convergence and suboptimal policy learning. To address these gaps, we propose DePSAC -- a Delay and Profit-aware Slice Admission Control scheme. Our DRL-based approach incorporates a delay-aware reward function, where penalties due to service delay incentivize the prioritization of latency-critical slices such as URLLC. Additionally, we employ Boltzmann exploration to achieve smoother and faster convergence. We implement and evaluate DePSAC on a simulated 5G core network substrate with realistic Network Slice Request (NSLR) arrival patterns. Experimental results demonstrate that our method outperforms the DSARA baseline in terms of overall profit, reduced URLLC slice delays, improved acceptance rates, and improved resource consumption. These findings validate the effectiveness of the proposed DePSAC in achieving better QoS-profit trade-offs for practical 5G network slicing scenarios.

Monte-Carlo Tree Search (MCTS) methods, such as Upper Confidence Bound applied to Trees (UCT), are instrumental to automated planning techniques. However, UCT can be slow to explore an optimal action when it initially appears inferior to other actions. Maximum ENtropy Tree-Search (MENTS) incorporates the maximum entropy principle into an MCTS approach, utilising Boltzmann policies to sample actions, naturally encouraging more exploration. In this paper, we highlight a major limitation of MENTS: optimal actions for the maximum entropy objective do not necessarily correspond to optimal actions for the original objective. We introduce two algorithms, Boltzmann Tree Search (BTS) and Decaying ENtropy Tree-Search (DENTS), that address these limitations and preserve the benefits of Boltzmann policies, such as allowing actions to be sampled faster by using the Alias method. Our empirical analysis shows that our algorithms show consistent high performance across several benchmark domains, including the game of Go.

Reinforcement learning (RL) algorithms aim to balance exploiting the current best strategy with exploring new options that could lead to higher rewards. Most common RL algorithms use undirected exploration, i.e., select random sequences of actions. Exploration can also be directed using intrinsic rewards, such as curiosity or model epistemic uncertainty. However, effectively balancing task and intrinsic rewards is challenging and often task-dependent. In this work, we introduce a framework, MaxInfoRL, for balancing intrinsic and extrinsic exploration. MaxInfoRL steers exploration towards informative transitions, by maximizing intrinsic rewards such as the information gain about the underlying task. When combined with Boltzmann exploration, this approach naturally trades off maximization of the value function with that of the entropy over states, rewards, and actions. We show that our approach achieves sublinear regret in the simplified setting of multi-armed bandits. We then apply this general formulation to a variety of off-policy model-free RL methods for continuous state-action spaces, yielding novel algorithms that achieve superior performance across hard exploration problems and complex scenarios such as visual control tasks.

The results provide useful insights to the understanding of Boltzmann exploration and multi-armed bandits - The paper is clearly written Cons: - The technique is incremental, and the technical contribution to multi-armed bandit research is small. The paper studiee Boltzmann exploration heuristic for reinforcement learning, namely use empirical means and exponential weight to probabilistically select actions (arms) in the context of multi-armed bandit. The purpose of the paper is to achieve property theoretical understanding of the Boltzmann exploration heuristic. I view that the paper achieves this goal by several useful results. First, the authors show that the standard Boltzmann heuristic may not achieve good learning result, in fact, the regret could be linear, when using monotone learning rates.

Despite its widespread use, there is virtually no theoretical understanding about the limitations or the actual benefits of this exploration scheme.

Large language models demonstrate remarkable capabilities after learning from enormous volumes of text data (Anil et al., 2023; Hoffmann et al., 2022; OpenAI, 2023). Yet, reinforcement learning from human feedback (RLHF) greatly improves their behavior even after only tens of thousands of interactions (Bai et al., 2022; Glaese et al., 2022; Ouyang et al., 2022; Stiennon et al., 2020). The uptake of chatbots affords opportunities to gather increasing volumes of human feedback, with each engagement eliciting expressions of satisfaction or preference (OpenAI, 2022). It is natural to wonder what new capabilities may emerge with this growing source of data. Superhuman ingenuity remains an alluring possibility. With increasing volumes, more can be inferred from human feedback.

This paper introduces single-partition adaptive Q-learning (SPAQL), an algorithm for model-free episodic reinforcement learning (RL), which adaptively partitions the state-action space of a Markov decision process (MDP), while simultaneously learning a time-invariant policy (i. e., the mapping from states to actions does not depend explicitly on the episode time step) for maximizing the cumulative reward. The trade-off between exploration and exploitation is handled by using a mixture of upper confidence bounds (UCB) and Boltzmann exploration during training, with a temperature parameter that is automatically tuned as training progresses. The algorithm is an improvement over adaptive Q-learning (AQL). It converges faster to the optimal solution, while also using fewer arms. Tests on episodes with a large number of time steps show that SPAQL has no problems scaling, unlike AQL. Based on this empirical evidence, we claim that SPAQL may have a higher sample efficiency than AQL, thus being a relevant contribution to the field of efficient model-free RL methods.

We present a general method for fitting finite mixture models (FMM). Learning in a mixture model consists of finding the most likely cluster assignment for each data-point, as well as finding the parameters of the clusters themselves. In many mixture models, this is difficult with current learning methods, where the most common approach is to employ monotone learning algorithms e.g. the conventional expectation-maximisation algorithm. While effective, the success of any monotone algorithm is crucially dependant on good parameter initialisation, where a common choice is $K$-means initialisation, commonly employed for Gaussian mixture models. For other types of mixture models, the path to good initialisation parameters is often unclear and may require a problem-specific solution. To this end, we propose a general heuristic learning algorithm that utilises Boltzmann exploration to assign each observation to a specific base distribution within the mixture model, which we call Boltzmann exploration expectation-maximisation (BEEM). With BEEM, hard assignments allow straight forward parameter learning for each base distribution by conditioning only on its assigned observations. Consequently, it can be applied to mixtures of any base distribution where single component parameter learning is tractable. The stochastic learning procedure is able to escape local optima and is thus insensitive to parameter initialisation. We show competitive performance on a number of synthetic benchmark cases as well as on real-world datasets.