First provide a summary of the paper, and then address the following criteria: Quality, clarity, originality and significance. It presents a slight modification of the NAC algorithm, where the original algorithm is a special case which is called forgetful NAC. The authors show that forget full Nac and optimistic policy iteration are equivalent. The authors also present a non-optimality result for soft-greedy Gibbs distribution, I.e., the optimal solution is not a fixed point of the policy iteration algorithm. I liked the unified view on both type of algorithms.

This paper addresses the scalability of symbolic planning under uncertainty with factored states and actions. Our first contribution is a symbolic implementation of Modified Policy Iteration (MPI) for factored actions that views policy evaluation as policy-constrained value iteration (VI). Unfortunately, a naïve approach to enforce policy constraints can lead to large memory requirements, sometimes making symbolic MPI worse than VI. We address this through our second and main contribution, symbolic Opportunistic Policy Iteration (OPI), which is a novel convergent algorithm lying between VI and MPI, that applies policy constraints if it does not increase the size of the value function representation, and otherwise performs VI backups. We also give a memory bounded version of this algorithm allowing a space-time tradeoff. Empirical results show significantly improved scalability over state-of-the-art symbolic planners.

The ability to generalise from a small number of examples is a fundamental challenge in machine learning. To tackle this challenge, we introduce an inductive logic programming (ILP) approach that combines negation and predicate invention. Combining these two features allows an ILP system to generalise better by learning rules with universally quantified body-only variables. We implement our idea in NOPI, which can learn normal logic programs with predicate invention, including Datalog programs with stratified negation. Our experimental results on multiple domains show that our approach can improve predictive accuracies and learning times.

Recently, remarkable progress has been made by approximating Nash equilibrium (NE), correlated equilibrium (CE), and coarse correlated equilibrium (CCE) through function approximation that trains a neural network to predict equilibria from game representations. Furthermore, equivariant architectures are widely adopted in designing such equilibrium approximators in normal-form games. In this paper, we theoretically characterize benefits and limitations of equivariant equilibrium approximators. For the benefits, we show that they enjoy better generalizability than general ones and can achieve better approximations when the payoff distribution is permutation-invariant. For the limitations, we discuss their drawbacks in terms of equilibrium selection and social welfare. Together, our results help to understand the role of equivariance in equilibrium approximators.

We address the scalability of symbolic planning under uncertainty with factored states and actions. Prior work has focused almost exclusively on factored states but not factored actions, and on value iteration (VI) compared to policy iteration (PI). Our first contribution is a novel method for symbolic policy backups via the application of constraints, which is used to yield a new efficient symbolic imple- mentation of modified PI (MPI) for factored action spaces. While this approach improves scalability in some cases, naive handling of policy constraints comes with its own scalability issues. This leads to our second and main contribution, symbolic Opportunistic Policy Iteration (OPI), which is a novel convergent al- gorithm lying between VI and MPI. The core idea is a symbolic procedure that applies policy constraints only when they reduce the space and time complexity of the update, and otherwise performs full Bellman backups, thus automatically adjusting the backup per state. We also give a memory bounded version of this algorithm allowing a space-time tradeoff. Empirical results show significantly improved scalability over the state-of-the-art.