Learning With Opponent-Learning Awareness (LOLA) (Foerster et al. [2018a]) is a multi-agent reinforcement learning algorithm that typically learns reciprocity-based cooperation in partially competitive environments. However, LOLA often fails to learn such behaviour on more complex policy spaces parameterized by neural networks, partly because the update rule is sensitive to the policy parameterization. This problem is especially pronounced in the opponent modeling setting, where the opponent's policy is unknown and must be inferred from observations; in such settings, LOLA is ill-specified because behaviorally equivalent opponent policies can result in non-equivalent updates. To address this shortcoming, we reinterpret LOLA as approximating a proximal operator, and then derive a new algorithm, proximal LOLA (POLA), which uses the proximal formulation directly. Unlike LOLA, the POLA updates are parameterization invariant, in the sense that when the proximal objective has a unique optimum, behaviorally equivalent policies result in behaviorally equivalent updates. We then present practical approximations to the ideal POLA update, which we evaluate in several partially competitive environments with function approximation and opponent modeling. This empirically demonstrates that POLA achieves reciprocity-based cooperation more reliably than LOLA.

Learning With Opponent-Learning Awareness (LOLA) (Foerster et al. [2018a]) is a multi-agent reinforcement learning algorithm that typically learns reciprocity-based cooperation in partially competitive environments. However, LOLA often fails to learn such behaviour on more complex policy spaces parameterized by neural networks, partly because the update rule is sensitive to the policy parameterization. This problem is especially pronounced in the opponent modeling setting, where the opponent's policy is unknown and must be inferred from observations; in such settings, LOLA is ill-specified because behaviorally equivalent opponent policies can result in non-equivalent updates. To address this shortcoming, we reinterpret LOLA as approximating a proximal operator, and then derive a new algorithm, proximal LOLA (POLA), which uses the proximal formulation directly. Unlike LOLA, the POLA updates are parameterization invariant, in the sense that when the proximal objective has a unique optimum, behaviorally equivalent policies result in behaviorally equivalent updates.

Learning With Opponent-Learning Awareness (LOLA) (Foerster et al. [2018a]) is a multi-agent reinforcement learning algorithm that typically learns reciprocity-based cooperation in partially competitive environments. However, LOLA often fails to learn such behaviour on more complex policy spaces parameterized by neural networks, partly because the update rule is sensitive to the policy parameterization. This problem is especially pronounced in the opponent modeling setting, where the opponent's policy is unknown and must be inferred from observations; in such settings, LOLA is ill-specified because behaviorally equivalent opponent policies can result in non-equivalent updates. To address this shortcoming, we reinterpret LOLA as approximating a proximal operator, and then derive a new algorithm, proximal LOLA (POLA), which uses the proximal formulation directly. Unlike LOLA, the POLA updates are parameterization invariant, in the sense that when the proximal objective has a unique optimum, behaviorally equivalent policies result in behaviorally equivalent updates.

The universe involves many independent co-learning agents as an ever-evolving part of our observed environment. Yet, in practice, Multi-Agent Reinforcement Learning (MARL) applications are usually constrained to small, homogeneous populations and remain computationally intensive. In this paper, we study how large heterogeneous populations of learning agents evolve in normal-form games. We show how, under assumptions commonly made in the multi-armed bandit literature, Multi-Agent Policy Gradient closely resembles the Replicator Dynamic, and we further derive a fast, parallelizable implementation of Opponent-Learning Awareness tailored for evolutionary simulations. This enables us to simulate the evolution of very large populations made of heterogeneous co-learning agents, under both naive and advanced learning strategies. We demonstrate our approach in simulations of 200,000 agents, evolving in the classic games of Hawk-Dove, Stag-Hunt, and Rock-Paper-Scissors. Each game highlights distinct ways in which Opponent-Learning Awareness affects evolution.

In the coming years, AI agents will be used for making more complex decisions, including in situations involving many different groups of people. One big challenge is that AI agent tends to act in its own interest, unlike humans who often think about what will be the best for everyone in the long run. In this paper, we explore a method to get self-interested agents to work towards goals that benefit society as a whole. We propose a method to add a manager agent to mediate agent interactions by assigning incentives to certain actions. We tested our method with a supply-chain management problem and showed that this framework (1) increases the raw reward by 22.2%, (2) increases the agents' reward by 23.8%, and (3) increases the manager's reward by 20.1%.

Emergent cooperation among self-interested individuals is a widespread phenomenon in the natural world, but remains elusive in interactions between artificially intelligent agents. Instead, na\"ive reinforcement learning algorithms typically converge to Pareto-dominated outcomes in even the simplest of social dilemmas. An emerging class of opponent-shaping methods have demonstrated the ability to reach prosocial outcomes by influencing the learning of other agents. However, they rely on higher-order derivatives through the predicted learning step of other agents or learning meta-game dynamics, which in turn rely on stringent assumptions over opponent learning rules or exponential sample complexity, respectively. To provide a learning rule-agnostic and sample-efficient alternative, we introduce Reciprocators, reinforcement learning agents which are intrinsically motivated to reciprocate the influence of an opponent's actions on their returns. This approach effectively seeks to modify other agents' $Q$-values by increasing their return following beneficial actions (with respect to the Reciprocator) and decreasing it after detrimental actions, guiding them towards mutually beneficial actions without attempting to directly shape policy updates. We show that Reciprocators can be used to promote cooperation in a variety of temporally extended social dilemmas during simultaneous learning.

Multi-agent settings are quickly gathering importance in machine learning. This includes a plethora of recent work on deep multi-agent reinforcement learning, but also can be extended to hierarchical RL, generative adversarial networks and decentralised optimisation. In all these settings the presence of multiple learning agents renders the training problem non-stationary and often leads to unstable training or undesired final results. We present Learning with Opponent-Learning Awareness (LOLA), a method in which each agent shapes the anticipated learning of the other agents in the environment. The LOLA learning rule includes an additional term that accounts for the impact of one agent's policy on the anticipated parameter update of the other agents. Preliminary results show that the encounter of two LOLA agents leads to the emergence of tit-for-tat and therefore cooperation in the iterated prisoners' dilemma, while independent learning does not. In this domain, LOLA also receives higher payouts compared to a naive learner, and is robust against exploitation by higher order gradient-based methods. Applied to repeated matching pennies, LOLA agents converge to the Nash equilibrium. In a round robin tournament we show that LOLA agents can successfully shape the learning of a range of multi-agent learning algorithms from literature, resulting in the highest average returns on the IPD. We also show that the LOLA update rule can be efficiently calculated using an extension of the policy gradient estimator, making the method suitable for model-free RL. This method thus scales to large parameter and input spaces and nonlinear function approximators. We also apply LOLA to a grid world task with an embedded social dilemma using deep recurrent policies and opponent modelling. Again, by explicitly considering the learning of the other agent, LOLA agents learn to cooperate out of self-interest.