CoFiI2P: Coarse-to-Fine Correspondences for Image-to-Point Cloud Registration

Image-to-point cloud (I2P) registration is a fundamental task in the fields of robot navigation and mobile mapping. Existing I2P registration works estimate correspondences at the point-to-pixel level, neglecting the global alignment. However, I2P matching without high-level guidance from global constraints may converge to the local optimum easily. To solve the problem, this paper proposes CoFiI2P, a novel I2P registration network that extracts correspondences in a coarse-to-fine manner for the global optimal solution. First, the image and point cloud are fed into a Siamese encoder-decoder network for hierarchical feature extraction. Then, a coarse-to-fine matching module is designed to exploit features and establish resilient feature correspondences. Specifically, in the coarse matching block, a novel I2P transformer module is employed to capture the homogeneous and heterogeneous global information from image and point cloud. With the discriminate descriptors, coarse super-point-to-super-pixel matching pairs are estimated. In the fine matching module, point-to-pixel pairs are established with the super-point-to-super-pixel correspondence supervision. Finally, based on matching pairs, the transform matrix is estimated with the EPnP-RANSAC algorithm. Extensive experiments conducted on the KITTI dataset have demonstrated that CoFiI2P achieves a relative rotation error (RRE) of 2.25 degrees and a relative translation error (RTE) of 0.61 meters. These results represent a significant improvement of 14% in RRE and 52% in RTE compared to the current state-of-the-art (SOTA) method. The demo video for the experiments is available at https://youtu.be/TG2GBrJTuW4. The source code will be public at https://github.com/kang-1-2-3/CoFiI2P.

Learning to Manipulate a Commitment Optimizer

It is shown in recent studies that in a Stackelberg game the follower can manipulate the leader by deviating from their true best-response behavior. Such manipulations are computationally tractable and can be highly beneficial for the follower. Meanwhile, they may result in significant payoff losses for the leader, sometimes completely defeating their first-mover advantage. A warning to commitment optimizers, the risk these findings indicate appears to be alleviated to some extent by a strict information advantage the manipulations rely on. That is, the follower knows the full information about both players' payoffs whereas the leader only knows their own payoffs. In this paper, we study the manipulation problem with this information advantage relaxed. We consider the scenario where the follower is not given any information about the leader's payoffs to begin with but has to learn to manipulate by interacting with the leader. The follower can gather necessary information by querying the leader's optimal commitments against contrived best-response behaviors. Our results indicate that the information advantage is not entirely indispensable to the follower's manipulations: the follower can learn the optimal way to manipulate in polynomial time with polynomially many queries of the leader's optimal commitment.

Optimal Private Payoff Manipulation against Commitment in Extensive-form Games

To take advantage of strategy commitment, a useful tactic of playing games, a leader must learn enough information about the follower's payoff function. However, this leaves the follower a chance to provide fake information and influence the final game outcome. Through a carefully contrived payoff function misreported to the learning leader, the follower may induce an outcome that benefits him more, compared to the ones when he truthfully behaves. We study the follower's optimal manipulation via such strategic behaviors in extensive-form games. Followers' different attitudes are taken into account. An optimistic follower maximizes his true utility among all game outcomes that can be induced by some payoff function. A pessimistic follower only considers misreporting payoff functions that induce a unique game outcome. For all the settings considered in this paper, we characterize all the possible game outcomes that can be induced successfully. We show that it is polynomial-time tractable for the follower to find the optimal way of misreporting his private payoff information. Our work completely resolves this follower's optimal manipulation problem on an extensive-form game tree.

On the Complexity of Computing Markov Perfect Equilibrium in General-Sum Stochastic Games

Similar to the role of Markov decision processes in reinforcement learning, Stochastic Games (SGs) lay the foundation for the study of multi-agent reinforcement learning (MARL) and sequential agent interactions. In this paper, we derive that computing an approximate Markov Perfect Equilibrium (MPE) in a finite-state discounted Stochastic Game within the exponential precision is \textbf{PPAD}-complete. We adopt a function with a polynomially bounded description in the strategy space to convert the MPE computation to a fixed-point problem, even though the stochastic game may demand an exponential number of pure strategies, in the number of states, for each agent. The completeness result follows the reduction of the fixed-point problem to {\sc End of the Line}. Our results indicate that finding an MPE in SGs is highly unlikely to be \textbf{NP}-hard unless \textbf{NP}=\textbf{co-NP}. Our work offers confidence for MARL research to study MPE computation on general-sum SGs and to develop fruitful algorithms as currently on zero-sum SGs.