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Title: CM3: Cooperative Multi-goal Multi-stage Multi-agent Reinforcement Learning

Paper content:
A variety of cooperative multi-agent control problems require agents to achieve individual goals while contributing to collective success.
This multi-goal multi-agent setting poses difficulties for recent algorithms, which primarily target settings with a single global reward, due to two new challenges: efficient exploration for learning both individual goal attainment and cooperation for others' success, and credit-assignment for interactions between actions and goals of different agents.
To address both challenges, we restructure the problem into a novel two-stage curriculum, in which single-agent goal attainment is learned prior to learning multi-agent cooperation, and we derive a new multi-goal multi-agent policy gradient with a credit function for localized credit assignment.
We use a function augmentation scheme to bridge value and policy functions across the curriculum.
The complete architecture, called CM3, learns significantly faster than direct adaptations of existing algorithms on three challenging multi-goal multi-agent problems: cooperative navigation in difficult formations, negotiating multi-vehicle lane changes in the SUMO traffic simulator, and strategic cooperation in a Checkers environment.
Many real-world scenarios that require cooperation among multiple autonomous agents are multi-goal multi-agent control problems: each agent needs to achieve its own individual goal, but the global optimum where all agents succeed is only attained when agents cooperate to allow the success of other agents.
In autonomous driving, multiple vehicles must execute cooperative maneuvers when their individual goal locations and nominal trajectories are in conflict (e.g., double lane merges) (Cao et al., 2013) .
In social dilemmas, mutual cooperation has higher global payoff but agents' individual goals may lead to defection out of fear or greed (Van Lange et al., 2013) .
Even settings with a global objective that seem unfactorizable can be formulated as multi-goal problems: in Starcraft II micromanagement, a unit that gathers resources must not accidentally jeopardize a teammate's attempt to scout the opponent base (Blizzard Entertainment, 2019) ; in traffic flow optimization, different intersection controllers may have local throughput goals but must cooperate for high global performance (Zhang et al., 2019) .
While the framework of multi-agent reinforcement learning (MARL) (Littman, 1994; Stone and Veloso, 2000; Shoham et al., 2003) has been equipped with methods in deep reinforcement learning (RL) (Mnih et al., 2015; Lillicrap et al., 2016) and shown promise on high-dimensional problems with complex agent interactions (Lowe et al., 2017; Mordatch and Abbeel, 2018; Foerster et al., 2018; Lin et al., 2018; Srinivasan et al., 2018) , learning multi-agent cooperation in the multi-goal scenario involves significant open challenges.
First, given that exploration is crucial for RL (Thrun, 1992) and even more so in MARL with larger state and joint action spaces, how should agents explore to learn both individual goal attainment and cooperation for others' success?
Uniform random exploration is common in deep MARL (Hernandez-Leal et al., 2018) but can be highly inefficient as the value of cooperative actions may be discoverable only in small regions of state space where cooperation is needed.
Furthermore, the conceptual difference between attaining one's own goal and cooperating for others' success calls for more modularized and targeted approaches.
Second, while there are methods for multi-agent credit assignment when all agents share a single goal (i.e., a global reward) (Chang et al., 2004; Foerster et al., 2018; Nguyen et al., 2018) , and while one could treat the cooperative multi-goal scenario as a problem with a single joint goal, this coarse approach makes it extremely difficult to evaluate the impact of an agent's action on another agent's success.
Instead, the multi-goal scenario can benefit from fine-grained credit assignment that leverages available structure in action-goal interactions, such as local interactions where only few agents affect another agent's goal attainment at any time.
Given these open challenges, our paper focuses on the cooperative multi-goal multi-agent setting where each agent is assigned a goal 1 and must learn to cooperate with other agents with possibly different goals.
To tackle the problems of efficient exploration and credit assignment in this complex problem setting, we develop CM3, a novel general framework involving three synergistic components:
1. We approach the difficulty of multi-agent exploration from a novel curriculum learning perspective, by first training an actor-critic pair to achieve different goals in an induced single-agent setting (Stage 1), then using them to initialize all agents in the multi-agent environment (Stage 2).
The key insight is that agents who can already act toward individual objectives are better prepared for discovery of cooperative solutions with additional exploration once other agents are introduced.
In contrast to hierarchical learning where sub-goals are selected sequentially in time (Sutton et al., 1999) , all agents act toward their goals simultaneously in Stage 2 of our curriculum.
2. Observing that a wide array of complex MARL problems permit a decomposition of agents' observations and state vectors into components of self, others, and non-agent specific environment information (Hernandez-Leal et al., 2018) , we employ function augmentation to bridge Stages 1-2: we reduce the number of trainable parameters of the actor-critic in Stage 1 by limiting their input space to the part that is sufficient for single-agent training, then augment the architecture in Stage 2 with additional inputs and trainable parameters for learning in the multi-agent environment.
3. We propose a credit function, which is an action-value function that specifically evaluates actiongoal pairs, for localized credit assignment in multi-goal MARL.
We use it to derive a multi-goal multi-agent policy gradient for Stage 2.
In synergy with the curriculum, the credit function is constructed via function augmentation from the critic in Stage 1.
We evaluate our method on challenging multi-goal multi-agent environments with high-dimensional state spaces: cooperative navigation with difficult formations, double lane merges in the SUMO simulator (Lopez et al., 2018) , and strategic teamwork in a Checkers game.
CM3 solved all domains significantly faster than IAC and COMA (Tan, 1993; Foerster et al., 2018) , and solved four out of five environments significantly faster than QMIX (Rashid et al., 2018) .
Exhaustive ablation experiments show that the combination of all three components is crucial for CM3's overall high performance.
CM3 finds optimal or near-optimal policies significantly faster than IAC and COMA on all domains, and performs significantly higher than QMIX in four out of five.
We report absolute runtime in Appendix F and account for CM3's Stage 1 episodes (Appendix J) when comparing sample efficiency.
Main comparison.
Over all cooperative navigation scenarios (Figures 5a to 5c), CM3 (with 1k episodes in Stage 1) converged more than 15k episodes faster than IAC.
IAC reached the same final performance as CM3 because dense individual rewards simplifies the learning problem for IAC's fully decentralized approach, but CM3 benefited significantly from curriculum learning, as evidenced by comparison to "Direct" in Figure 5f .
QMIX and COMA settled at suboptimal behavior.
Both learn global critics that use all goals as input, in contrast to CM3 and IAC that process each goal separately.
This indicates the difficulty of training agents for individual goals under a purely global approach.
While COMA was shown to outperform IAC in SC2 micromanagement where IAC must learn from a single team reward (Foerster et al., 2018) , our IAC agents have access to individual rewards that resolve the credit assignment issue and improve performance (Singh et al., 2019) .
In SUMO (Figure 5d ), CM3 and QMIX found cooperative solutions with performances within the margin of error, while COMA and IAC could not break out of local optima where vehicles move straight but do not perform merge maneuvers.
Since initial states force agents into the region of state space requiring cooperation, credit assignment rather than exploration is the dominant challenge, which CM3 addressed via the credit function, as evidenced in Figure 5i .
IAC underperformed because SUMO requires a longer sequence of cooperative actions and gave much sparser rewards than the "Merge" scenario in cooperative navigation.
We also show that centralized training of merely two decentralized agents allows them to generalize to settings with much heavier traffic (Appendix E).
In Checkers (Figure 5e ), CM3 (with 5k episodes in Stage 1) converged 10k episodes faster than COMA and QMIX to the global optimum with score 24.
Both exploration of the combinatorially large joint trajectory space and credit assignment for path clearing are challenges that CM3 successfully addressed.
COMA only solved Checkers among all domains, possibly because the small bounded environment alleviates COMA's difficulty with individual goals in large state spaces.
IAC underperformed all centralized learning methods because cooperative actions that give no instantaneous reward are hard for selfish agents to discover in Checkers.
These results demonstrate CM3's ability to attain individual goals and find cooperative solutions in diverse multi-agent systems.
Ablations.
The significantly better performance of CM3 versus "Direct" (Figures 5f to 5j) shows that learning individual goal attainment prior to learning multi-agent cooperation, and initializing Stage 2 with Stage 1 parameters, are crucial for improving learning speed and stability.
It gives evidence that while global action-value and credit functions may be difficult to train from scratch, function augmentation significantly eases the learning problem.
While "QV" initially learns quickly to attain individual goals, it does so at the cost of frequent collisions, higher variance, and inability to maintain a cooperative solution, giving clear evidence for the necessity of the credit function.
We presented CM3, a general framework for cooperative multi-goal MARL.
CM3 addresses the need for efficient exploration to learn both individual goal attainment and cooperation, via a two-stage curriculum bridged by function augmentation.
It achieves local credit assignment between action and goals using a credit function in a multi-goal policy gradient.
In diverse experimental domains, CM3 attains significantly higher performance, faster learning, and overall robustness than existing MARL methods, displaying strengths of both independent learning and centralized credit assignment while avoiding shortcomings of existing methods.
Ablations demonstrate each component is crucial to the whole framework.
Our results motivate future work on analyzing CM3's theoretical properties and generalizing to inhomogeneous systems or settings without known goal assignments.
Hernandez-Leal, P., Kartal, B., and Taylor Tampuu, A., Matiisen, T., Kodelja, D., Kuzovkin, I., Korjus, K., Aru, J., Aru, J., and Vicente, R. Instantiate N > 1 agents 8: Set all target network weights to equal main networks weights 13:
Initialize exploration parameter = start and empty replay buffer B

assistant: text: A modular method for fully cooperative multi-goal multi-agent reinforcement learning, based on curriculum learning for efficient exploration and credit assignment for action-goal interactions.