David Milec, Spyridon Samothrakis, Michael Fairbank +1cs.LG cs.AI
The dominance of Neural Networks (NNs) in RL is partially due to their incremental learning capability, which naturally suits the online, non-stationary nature of self-play training. However, gradient-boosted trees like LightGBM are widely recognised as the state of the art for tabular data in supervised learning, often outperforming NNs in accuracy and efficiency. Game states are inherently tabular---discrete actions, categorical card identities, structured board positions---which makes them an ideal candidate for tree-based methods. We introduce LUGL (Local Updates, Global Learning), a framework that decouples data collection from model fitting, enabling non-incremental learners such as GBTs to operate in RL settings where they would otherwise fail due to distributional shift. LUGL alternates between a local updates phase, where the agent plays self-play games and accumulates tabular updates (Q-values, V-values, policies, or regret values) in a finite table, and a global learning phase, where the table is used to train a function approximator that generalises to unseen states before the table is reset. We test our approach in four standard perfect-information games (Tic-tac-toe, Connect-4, Othello, and Hex) and five imperfect-information games (Kuhn's poker, Leduc Hold'em, Liar's Dice, Goofspiel, and Flop5 Hold'em), and show that our results are competitive with or superior to DQN and DeepCFR. Our experiments demonstrate that the community's strong bias towards NNs in game-playing may be unwarranted, since LightGBM-based agents achieve competitive or superior performance across all tested benchmarks.
For finite-horizon tabular CVaR reinforcement learning, prior work proves a $\widetilde{O}(τ^{-1}\sqrt{SAK})$ leading regret bound for arbitrary normalized return laws and the sharper $\widetilde{O}(\sqrt{SAK/τ})$ rate under a density lower bound. We show that the same Bernstein CVaR-UCBVI algorithm attains the sharper rate without continuity assumptions. The key is a selected-budget self-bound: the conditional variance of the episode shortfall is at most $τ$ plus the value-estimation width. Substitution into the original Bernstein decomposition yields, with high probability, $\widetilde{O}(\sqrt{SAK/τ}+(SAHK^{1/4}+S^2AH)/τ)$ regret for arbitrary normalized return laws, including atomic, mixed, and continuous laws. The $τ^{-1/2}$ leading term matches the expected-regret minimax lower bound up to logarithmic factors. Thus Bernstein CVaR-UCBVI is minimax-optimal over the full return-law class in the leading-order regime; the lower-order terms retain their $τ^{-1}$ dependence.
Q-learning is a fundamental algorithm in reinforcement learning (RL) for solving discounted Markov decision processes (MDPs) when the transition kernel is unknown. The deep Q-network (DQN) extends Q-learning by using a deep neural network for Q-function approximation, which makes Q-learning applicable to more practical high-dimensional problems. Dueling Q-learning decomposes the Q-function into a value function and an advantage function and learns the two components jointly, which can improve learning efficiency. However, the theoretical understanding of dueling Q-learning is still limited. Recent work has initiated an analysis of tabular dueling Q-learning, but existing guarantees focus on a regularized formulation and leave the pure tabular update less completely understood. This paper strengthens that line of analysis by adding a direct interpretation of the centered tabular decomposition and by establishing convergence guarantees for the unregularized, unprojected constant step-size recursion. In particular, we derive an exact switching linear system representation for deterministic dueling Q-learning and a finite-time error bound in expectation for the sampled stochastic version. The analysis clarifies how the value and advantage updates act as different gains on the action-common (value function) and action-differential (advantage function) components of the Q-function.
The asymptotic behaviour of Monte Carlo Exploring Starts (MCES) is a long-standing open question in reinforcement learning, even in the tabular setting. We investigated the convergence properties of tabular MCES by constructing examples in which the algorithm converges to suboptimal solutions. This paper presents new counterexamples for both initial-visit and first-visit MCES and gives a convergence-restoring modification for the initial-visit case. We show that stable suboptimal solutions may exist for initial-visit MCES with sample-average updates even when greedy actions are updated more often than non-greedy actions on average. However, by scaling learning rates inversely to update frequencies on a state-by-state basis, convergence to optimality is guaranteed. Unlike previous uniformisation methods, this modification is applicable to large-scale problems that require approximating the estimated value function. We then extend the example to show that sample-average first-visit MCES may also converge to suboptimal solutions. This largely settles a fundamental open problem and shows that exploring starts alone do not guarantee convergence to optimality. More broadly, these results highlight that convergence depends critically on the relative size and frequency of updates applied to different actions, making the choice of learning rates and the balance between exploration and exploitation central to the analysis of MCES and the implementation of scalable Monte Carlo control methods.