Opponent Modeling based on Subgoal Inference
Authors: XiaoPeng Yu
Jiechuan Jiang
Zongqing Lu
Venue: NeurIPS 2024 poster (2024)
Keywords: multi-agent
deep reinforment learning
Primary area: reinforcement_learning
TL;DR: We introduce a novel method for opponent modeling based on subgoal inference.

Abstract: When an agent is in a multi-agent environment, it may face previously unseen opponents, and it is a challenge to cooperate with other agents to accomplish the task together or to maximize its own rewards. Most opponent modeling methods deal with the non-stationarity caused by unknown opponent policies via predicting the opponent’s actions. However, focusing on the opponent’s action is shortsighted, which also constrains the adaptability to unknown opponents in complex tasks. In this paper, we propose opponent modeling based on subgoal inference, which infers the opponent’s subgoals through historical trajectories. As subgoals are likely to be shared by different opponent policies, predicting subgoals can yield better generalization to unknown opponents. Additionally, we design two subgoal selection modes for cooperative games and general-sum games respectively. Empirically, we show that our method achieves more effective adaptation than existing methods in a variety of tasks.

Opponent Modeling based on Subgoal Inference
Xiaopeng Yu
Jiechuan Jiang
Zongqing Lu
School of Computer Science, Peking University
Abstract
When agent is in multi-agent environment, it may face previously unseen opponents, and a challenge to cooperate with other agents to accomplish the task together to maximize its own rewards. Most opponent modeling methods deal with the non-stationarity caused by unknown opponent policies via predicting the opponent's actions. However, focusing on the opponent's 's action is shortsighted, which also constrains the adaptability to unknown opponents in complex tasks. In this paper, we propose opponent modeling based subgoal inference, which infers the opponent's 's subgoals through historical trajectories. As subgoals are likely be shared by different opponent policies, predicting subgoals can yield better generalization to unknown opponents. Additionally, we design two subgoal selection modes for cooperative games and general-sum games respectively. Empirically, we show that our method achieves more effective adaptation than existing methods in variety of tasks.
Introduction
Autonomous agents systems capable of making deci- sions and acting independently in their environment, often operating without direct human intervention [3]. These agents can either cooperate with or compete against each other, depending
the context. In cooperative scenar- ios, many multi-agent reinforcement learning (MARL) aim bridge the information gap between agents 44 by training agents in a central- ized manner, called centralized training with decentralized execution, enabling agents to work together seamlessly to accomplish cooperative tasks. Alternatively. fully de- centralized methods [17 [40] seek to break free from the constraints of centralized training, allowing agents reach collaboration in a simpler and decentralized manner. In competitive scenarios, NESP [5]. PSRO 19), and Deep- Nash (29] employ eelf-play to train agents for equilibrium strategies, allowing agents to adapt and improve their policy. By considering how the agent affects the expected learning progress of other agents, LOLA [10] and COLA [4] apply opponent shaping to this setting. Overall, these methods focus on training agents in way that accounts for their interactions, resulting in a set of policies that enable effective collaboration or competition within group of agents.
methods 20 41
33
38
Figure 1: Infer the goal of others
While the above methods emphasizes the collective behavior of agents, it also crucial consider the role of individual agents, particularly self-interested agents, in these multi-agent environments. welf-interested agent [37 12 operates with the primary goal of maximizing its own benefits,
"Correponndncee to zongging. luēpku. edu.
38th Conference on Neural Information Processing Systems (NcurIPS 2024).

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even when interacting with other agents, When the objectives of self-interested agent align with those of the team, this scenario falls under ad-hoc teamwork [2T
8
39
however, in more general
A key technique for self-interested agents in such settings is opponent modeling 24 3 which enables them to analyze
cases, these interactions are framed as noncooperative games 34
23
45
and predict the actions, goals, and beliefs of other agents. By modeling the intentions and policies of other agents, the training process of the agent might be stabilized [27]. Many studies rely on predicting the actions [14 16 13 25 26), goals [32 311, and returns [42) of opponents during
training. Then, the autonomous agent can adapt to different or unseen opponents by using the predictions or representations that are produced by the relevant modules.
Although a lot of the existing methods concentrate on modeling the opponent's 's actions, we argue that such an approach is sigrt-sighted, pedantical, and highly complex. Generally, modeling an opponent's 's actions just predicts what it will do at the next step. Intuitively, it is more beneficial for the agent to make decisions if it knows the situation of the opponent several steps ahead. Predicting the actions over few steps has high uncertainty. For example, to reach the goal point of (2. 2), an opponent moves from (0, 0) following the action sequence <t, f. -, +> by four steps (Cartesian coordinates). But, there are also other action sequences, i.c., <t, -, 1.> t, +>; 1- -
< <-, 1. 1. t>, that can lead to the same goal. Obviously, the complexity and uncertainty of predicting the action sequence are much higher than the goal itself. Other methods that claim to predict the opponent's 's goal [61 32), but without explicitly making connection to the opponent's 's goal or just predicting the goal at the next step, are essentially as shortsighted as modeling actions.
Inspired by the fact that humans can predict the opponent's goal by observing the opponent's s actions for several steps as illustrated in Figure [ in this paper, we propose Opponent Modeling based on subGoals inference (OMG), which uses variational inference to predict the opponent's ' future subgoals from historical trajectories. The trajectory of an opponent's 's policy consists of a set of subgoals, and the trajectories of different policies may contain the same subgoals. This combinatorial property of the subgoals facilitates the generalization of the agent to unseen opponents' policies. Moreover, we design two manners for selecting subgoals, which are applied to cooperative games and general sum games, respectively. Empirically, OMG outperforms existing opponent modeling methods in a variety of multi-agent environments, demonstrating the superiority of inferring subgoals over predicting actions.
2 Related Work
Opponent modeling. Opponent modeling plays crucial role in enhancing the robustness and stability of reinforcement learning (27). Given the presence of diverse opponent policies in multi- agent environments, the autonomous agent faces a significant challenge in learning resilient policies. When an agent perceives opponent part of the environment, the resulting environment becomes inherently unstable and intricate. To address this challenge, one straightforward method involves equipping the agent with the ability to incorporate information about its opponent, including aspects like the opponent's ' behavior, goals, and beliefs 3. i.e., opponent modeling. It gives the agent a deeper insight and prediction ability about the opponent's policy. Thus, the autonomous agent views the environment as less unstable and can simply use single-agent reinforcement learning methods.
A common approach to modeling the policy of an opponent is predicting the opponent's 's actions. DRON 14] and DPIQN [16] extend DQN [22) by adding another network that estimates the opponents" actions from the observations. The DQN uses the hidden layer of this network to improve its policy. Variational auto-encoders can also be used to model the opponent's 's policy (25), which results in probabilistic representations instead of fixed vectors. PR2 [48] and TP-MCTS [7] combine the idea of recursive reasoning, nested form as "the agent believes [that the opponent believes (that the agent believes... "..] based on modeling the action of the opponent. Some works focus on modeling beliefs. [53] combined the sequential and hierarchical variational auto-encoders to construct a belief inference model using meta-learning, for belief inference. [5T] introduced landmarks into the behavior model and improved the model by the action sequence of the opponents, so as to recognize and compare the opponent's intention.
Another key aspect of opponent modeling to infer the opponent's goal. 5 formulated the goal recognition as a Markov decision process (MDP) and calculated the posterior probability of the

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Trajectories
Causal Relationships
C-1
Data
0
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St
Sc+1
S
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Parameter Update
RNN
FC
SubGoal Selector
VAE &
he
Opponent Model
policy network
Conditioned VAE
VAE 1/2
0e
(4)
ar argaax fw(()
policy network
S1+1
(.+ ae
phase
Update phase
SubGoal Selector
Figure 2: Diagram of OMG. During the interaction phase, OMG infers the subgoal from the historical trajectory. The CVAE acts as an inference model, deducing the opponent subgoal denoted as 9. The inferred subgoal serves as input for the policy model ((s, I, a). In the update phase, OMG examines the entire trajectory model. The subgoal selector employs value-based heuristic to choose state from the next few steps and then encodes into a subgoal using the pre- pre-trained VAE 15.
hindsight manner to select subgoals 9 as priors for training the inference
goal by Bayes' rule based on prior goal library. ToMnet 33 aims to give the agent a human-like Theory of Mind. It uses three networks to infer the agent's goal and action from previous and present information. SOM [32] implements the Theory Mind with a goal library from a different perspective. SOM uses its own policy, the opponent's 's observation, and the opponent's action to work backward to learn the opponent's goal distribution by gradient ascent. These methods either require a prior goal library infer implicit "goals" that not supervised by ground truth goals.
In some scenarios, opponents may continuously learn during interaction. Meta-MAPG [8] combines Meta-PG [ and LOLA (10), and focuses on the problem of the non-stationary environment caused by the continuous learning of opponents. MBOM (50) simultaneously targets variety of adversaries, fixed policy, continuous learning, by modeling the possible policies that an opponent may form, combined with Bayesian inference to generate an opponent's imagined policy. GSCU [I] chooses online between real-time greedy strategy and fixed conservative strategy through Bayesian belief' in competitive environments. Unlike these methods, in this paper, we consider the most common setting where opponents have unseen, diverse, but fixed policies during test.
Goal-conditioned RL. Goal-conditioned reinforcement learning an extension of the single-agent algorithm. Most works focus on learning coal-conditioned policy, where the goals are usually predefined 30 52 Some works consider acquiring subgoals automatically to accelerate learning.
(8 proposed method that uses expert trajectories to generate subgoals, while 7 proposed to incorporate imaginary subgoals into policy learning to facilitate learning complex tasks, where subgoals are measured by value functions. Unlike existing coal-conditioned RL methods, we aim to infer the subgoal of the opponent and condition the agent policy on the inferred subgoal.
3 Preliminaries
In general, we consider an n-agent stochastic game M = AS A", S is the state space, A' is the action space of agent i [L...., n1, A 11 A' is the joint action space of agents, P S x A x S > [0. 1] is transition function, Rd : A + R is the reward function of agent and 7 E [0, 1) the discount factor. The policy of agent T', and the joint
R", where
policy of other agents is π ([(s) 11 T (a']s), where -t is the joint action except agent
3

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i. All agents interact with the environment simultaneously without communication. The historical trajectory is available, i.e., for agent i at timestep t, Tr = {so, aj - ..... St-1, a:-1. - 1 is observable. The goal of the agent i is maximize expected cumulative discount rewards:
E
y (st
(1)
((ll,,,a 1). amdr (1a)).07 (-18a)
For convenience, the learning agent treats all other agents as a joint opponent with the joint action a ~ x. (-Is) and reward r- The action and reward of the learning agent are respectively denoted as (-|s)) and for notation simplicity.
an agent treats other agents as part of the environment and ignores the non-stationarity posed by the change of other agents' policies independent Q-learning 4 44 Its Q-function Q is updated by:
((5 ae) = Ep(sen (,,)) (r + max @(s++1,4)]-
(2)
Opponent modeling typically predicts the actions of other agents to address the non-stationary problem. The opponent model uses historical trajectory as input to predict ä- ~ ((|r),, where ä the estimate of a Then, its Q-function is updated as:
a aa) = Ep Bp (a,)) [r +
max ((s41..77111) a)].
(3)
Note that we cast our discussion here to Q-learning. All can be similarly applied to other RL methods, such as PPO [36].
4 Method
In this section, we present our method, opponent modeling based on subgoals inference (OMG). First, we discuss learning policies with the opponent's 's subgoals, compared to learning based on the opponent's s actions. Then, we introduce our opponent model that infers the opponent's 's subgoals using value-based heuristic.
4.1 Policy Learning with Opponent's Subgoals
In Equation B). the traditional opponent modeling with the opponent's actions is introduced. Here, we introduce policy learning with the opponent's ' subgoals.
The opponent's 's subgoals offer more structured representation compared to individual actions. Subgoals represent feature embeddings of future states that the opponent aims to achieve based on its policy. Although diverse action sequences can lead to the same state, focusing on subgoals provides higher-level understanding of the opponent's ' long-term intentions. Instead of gaining new information, subgoal modeling reinterprets observed data to emphasize long-term objectives, reducing variability and improving learning efficiency [24]. By concentrating on the opponent's 's desired states rather than individual actions, the agent can achieve more stable and effective policy learning.
The opponent's subgoal distribution is determined by the opponent's action sequence, i.e., the opponent's policy, but the subgoal space is still the representation of the state space. Here we decouple the subgoal from the opponent's policy and just consider dacision-making problems conditioned on the opponent's 's subgoal. Formally, we transform the original stochastic game A into a state- augmented MDP, defined by MMg (S, A P, R 7). where is the subgoal space. is representation of future states the opponent may go, [ S [S].
The atute-augmented MDP's state space S extends to the MDP with state-subgoal pairs (5,9). Therefore, the agent's 's Q-function based on the opponent's subgoal is updated as:
Q 9t. 04) Ep (ppssallsi.a..... (,,) [a)lr + max Q(s++1 St. a)).
(4)
Here the pair 18 9t) is used instead of (8++1, Sc+1 ), we assume that the next state of (st, gt) follows the same goal. In the framework of OMG, gr and g++1 will reach the same state at the end of the episode.

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max @(8,a=i,o)
IIBX (s.g9.
max ((8,a
maxX (8,,
(a) training steps 1e5
(h) training steps 1e7
Figure 3: Learned Q-values using tabular Q-learning in an 11 x 11 gridworld. The agent and the opponent start from the S₁ and S2, respectively. The two rewarding grids are D and D2 and the reward will only be given the agent who arrives first. The opponent executes one of policies Ti and n² which target Dj and D2, respectively. The g and a - are obtained from an oracle.
Q-values with opponent's subgoals are just effective with opponent's actions. We carry an experiment in an 11 x 11 gridworld with two agents, as detailed in Figure After convergence, the Q-value increases as the agent gets closer the rewarding grid, indicating meaningful Q-value with the opponent's subgoal, as shown in Figure ((b
Effective opponent's 's subgoals enhance policy learning. The Q-value using the opponent's action learns slower than the Q-value with the opponent's 's subgoal Figure resulting from the tuple (s, a a) is (s, a- a). the method using (s, g. a) naturally holds the advantage of faster learning than the method of (s,a=),
numerous than (s, 9, a.) in the Q-table. When there fewer (s, 9, a) than
The quantity of (8, 9: a.) is contingent upon the goal selection, and present analysis of the quantitative relationship between pair (s. g) and (s, a=)), see Appendix A In short, the number of (s, g) is significantly smaller than that of (s, a-²) in our method. Next, we explain how the opponent model secures these benefits.
4.2 Opponent Modeling Based on Subgoal Inference
Our opponent modeling consists of two components: subgoal inference model and subgoal selector. The subgoal inference model employs the historical trajectory to predict the opponent's subgoal, serving imput for the policy during the interaction phase. The subgoal selector scrutinizes the entire historical trajectory using a value-basee based heuristic to choose the appropriate subgoal for training the inference model during the update phase.
Subgoal inference model. The subgoal y represents a feature embedding of a future state. Specifi- cally, for trajectory (so, Op, 9g ...., ,t, at a, sT). the state corresponding to subgoal gi at is one of future states N₂ = {8141, S142.... selector.
denoted as sy and determined by the subgoal
The objective of the subgoal inference model is to infer It. from the historical trajectory T This aligns with the intuitive hypothesis that the opponent's intention can often be inferred after just few initial actions.
{sg, ag, ag St-1, a0-10-1000 Q0110 }
Here, we introduce variational inference and employ conditional variational auto-encoder (CVAE) as the subgoal inference model. In this model, we represent the subgoal posterior probability as (ā Fe, 8x) and the likelihood estimate as pa (sx (1, Tr) with e and 0 respectively denoting the network parameters. The subgoal prior model, denoted as Pv. is pre-trained variational autoencoder (VAE) using the states previously collected in the environment, and produces the subgoal prior Pv (guls?) given the subgoal state si chosen by the subgoal selector.
Further details about the network architecture are provided in Figure the subgoal inference model is:
The optimization objective of
0, ò > arg max E (oo
Po 0., [.) KLL (z)
(5)
0.6
5

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Algorithm OMG
1: Preparation:
2: Interact with V opponents to collect s and train the prior model Pv
3: Initialize subgoal inference model parameters and
4: Initialize Q-network Q and the replay buffer '
5: repeat
6: Interaction phase
7: Observe state
8:
Infer I by subgoal inference model ( 8)
9:
Choose action a by max, 2(s, g, a) with e-greedy
10:
Store experience (s, a rr) ) in replay buffer D
Update phase
12:
if time to update then
Obtain prior subgoal 9 by 6 or
14:
Calculate subgoal g by (8)
Update Q-newwork by
16:
Update subgoal inference model Ue and by 5
end if
18:
until convergence
where the term Pe (7 (9) in the KL divergence accounts for the prior distribution and is pre-trained. The purpose of including the KL divergence term is to prevent collapse of the inference model.
Subgoal selector. The primary objective the subgoal selector is to choose the appropriate future state of the subgoal state se from from,; input to the prior model. The choice of the subgoal state plays a significant role in shaping the agent's 's behavior and leaning towards either optimism or conservatism. This is especially critical when dealing with cooperative games and general-sum games, where the dynamics of interactions are complex and multifaceted. In these contexts, we provide two distinct manners for the subgoal selection:
Dt = arg max Ry (1e.) (le.)
ENN
9t arg min Eyypp())s) (i (8t.
a.EN?
where V(s. (s. g. a), NH is the set of future states (st+1,'.. S8+H) As discussed in Section 4.1 the quantity of (s, g) pairs is crucial. Selecting candidate subgoal states is pivotal in this states within the next H timesteps instead of all future states. The choice of H
regard. Thus, gives a tradeoff between the agent's generalization to diverse opponents induced by the fact that the subgoals of different trajectory fragments have combinatorial properties and the learning difficulty incurred by the increased opponent subgoals.
As indicated in Equation (6) pinpoint the subgoal within H -horizon that maximizes the V-value. The agent incorporates this to optimize the Q-function, thus adopting an optimistic strategy akin to the maximax strategy (6), which applies to cooperative games. Conversely, if choose the subgoal as in Equation (7). corresponds to the subgoal yielding the lowest value. The agent then employs this for learning Q-function, leading to conservative strategy similar to the minimax strategy, which is commonly used in general-sum games.
The subgoal selector and the subgoal inference model as whole constitute our opponent modeling module. During the interaction phase, the subgoal inference model used to get the inferred subgoal ÿ. which is combined with the state as the input to the Q-network. During the update phase, the prior subgoal ğ generated by the subgoal selector is provided to the inference model for training. The subgoal inference model is unstable at the beginning, which may disturb the updating of the Q-network. Therefore, we use the following combination of the prior subgoal and the inferred subgoal 9 as the input of Q-network.
St = TT > <) + geT S c),
U 1),
(8)
where is a hyperparameter that decreases to zero training. We will further empirically study this in Section 5.4
For completeness, the full procedure of OMG is given in Algorithm

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upisode_steps
121
score
LIM
PPO
11
10
OMG-optim
episode
141
Naivé
LIAM
D3ON
OME conserv OMG optm
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(a) Foraging
(b) Predator-Pre Prey
(a) Performance Foraging. The red bar shows the total score obtained by the agent. The blue bar illustrates the number of steps in each episode. The results show that OMG converge to the same score as the baselines but end the episode in fewer steps because it predicts the opponent's goal. (b) Performance in Predator-Prey. The results show the score obtained by the agent predator with two other uncontrolled predators, and OMG outperforms the baselines.
Figure 4:
5 Experiments
First, we evaluate OMG's training performance in two environments (discrete and continuous state spaces) and then test its generalization opponents with unseen policies in a more complex environment. In all the experiments, the baselines have the same neural network architectures as OMG. All the methods using mean and standard deviation. More details about experimental settings and hyperparameters are available in Appendix B To ensure reproducibility. we include the code in the supplementary material and will make it open-souree upon acceptance.
trained for five runs with different random seeds, and results presented
We experiment in the following three multi-agent environments. Foraging 2 is an 8 gridworld where the agent aims to collect foods. Predator-Pree [20) three-against-one scenario with continuous space where the agent collaborates with predators capture prey. SMAC (B5) is high- dimensional environment for collaborative multi-agent reinforcement learning based on StarCraft II, where the agent cooperates with of opponents with unknown policies to accomplish tasks.
5.1 Baselines
In the experiments, we implement two variants of OMG, OMG-optimistic and OMG-conservvttvv,, based on the subgoal selection manners in Equation (6) and Equation (7). respectively. OMG compared with the following methods:
Naïve OM uses observation to directly model the opponent's policy, which assists the agent in decision decision-making by predicting the opponent's actions.
LIAM 26 uses the observations and actions of the opponent with an encoder-decoder architecture, and the model learns to extract representations about the opponent, conditioned only on the local observations of the controlled agent.
D3QN PPO IQL 46
are classical RL algorithms without opponent modeling.
We use D3QN, PPO, and IQL as the backbone algorithms in Foraging, Predator-Prey, and SMAC, respectively, to reproduce the performance of baselines. The versions of OMG that are based on D3QN and IQL. incorporate "dueling" and "double" tricks over Algorithm [ For OMG based on PPO, please refer to Appendix for details.
5.2 Performance of Training
We evaluate the performance of OMG Foraging and Predator-Prey, and the results are shown in Fa) and Figure 4b)) respectively. In the foraging environment, our method attains similar scores to the baseline methods, and both the agent and the opponent achieve comparable scores.
7

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IQL
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Naive OM
OMG-conserv
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70.0%
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40.
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7 non aon-homllogue 5 homologue
homologue
0.0%
2 non homblogue homalogue
20.0%
homologue
(a) 8m
(b) 38 vz
2c 2___v__4222
3s vs "s_5z (b) and 2c_vs 2g_644gg_0 [c] maps of SMAC. The X-axis represents the opponent's policies, and "homologue" refers to the policy learned by the same algorithm, while "non-homologue" represents different ones; e.g. 7 homologue refers 7 opponents from agents trained by the same algorithm (QMIX, VDN IQL) on the 8m, and 7 non-homologue involves 7 opponents from different runs of those algorithms. The results show that OMG-optimistic outperforms all baselines. The results are averaged over collaborating with 30 opponents of different policies, with 95% confidence intervals.
Figure 5: Test performance of cooperation with unseen opponents in 8m (a)
OMG has shorter episode length compared to other methods because OMG can predict the subgoal that the opponent is heading to and thus avoid wasting steps in the same direction. In addition, the results show that OMG-conservative is more suitable than OMG-optimistic in this scenario since this a general-sum game. The baselines based on action modeling. LIAM and Naïve OM, demonstrate comparable performance, whereas D3QN without opponent modeling, exhibits subpar results. In the predator-pres environment, the agent acts as the predator and collaborates with the other two uncontrolled predators to catch the prey. The results in Figure 4(b) show that OMG obviously outperforms action modeling methods, which demonstrates that OMG can also work efficiently in continuous state space. PPO without opponent modeling can hardly improve performance training due to the non-stationarity caused by opponents. OMG-optimistic slightly performs better than OMG-conservative because OMG-optimistic is suitable for the cooperative game.
5.3 Generalization to Unknown Opponents
We evaluate the generalization of OMG in a more complex multi-agent environment, SMAC, which enables the opponents to exhibit more diverse policies. The experimental results of 8m, 3s vy vz_5 and 2c_vs_ ys various unknown opponents, resulting in poor performance, especially when the opponents non-homologue. This underscores the effectiveness opponent modeling in autonomous agent tasks. LIAM and Naïve OM, the action modeling methods, contribute the team's improved win rate some extent. The mediocre performance of OoGG-oonsevvative attributed to its overly cautious subgoal selection. OMG-conservativve is par with IQL, which is consistent with the "conservative" OMG-optimistic surpasses the baseline methods, indicating that OMG-optimistic can generalize well unknown collaborators through positive subgoal selection.
10_____6440 64zg are shown in Figure 5 Without opponent modeling. IQL struggles to adapt to
5.4 Ablation Study
The ablation study is conducted for the network structure of the inference model, subgoal selection, and hyperparameter horizon H. OMG uses CVAE as the inference model. Here, we instead employ supervised learning to train inference model using the subgoal selector's ' output Øt, obtained from either Equation (6) or Equation (7). This model is referred to as MMG-suuprvisee.. The results in the foraging environment are presented in Figure 6(a) The results indicate that OMG-optimistic and OMG-conservative outperform their counterparts, which is attributed to enhanced adaptability of variational inference to the uncertainty in the opponent's 's policy. Dealing with multiple opponents employing distinet policies poses challenge for supervised learning, as establishing a mapping relationship between historical trajectories and subgoals becomes intricate.

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12.3
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eplovee Stea
etiodd strpe
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pcore
spti
sap--raarre ORG--AT7--p55 ApS
DMG OMG-4pon apain
candann
(a) Inference model architectures
(b) Subgoal selection strategies
Figure 6: Ablation study in Foraging. In (a) methods on the X-axis labeled with "supv" indicate that the inference model uses MLP instead of CVAE. In MMG-ranmmn OMG-Is, and OMG-3s represent subgoals selected from opponent's future states: randomly, at the next step, and third step, respectively.
eplondss
ep sosodes
esboads
eplsndes
(a) Score
(b) Episode length
(c) Score
(d) Episode length
Figure 7: Ablation study of OMG in Foraging. (a) and (b)
compares OMGs with different subgoal
inputs for policy learning. (c) and (d) show ablation study for the hyperparameter horizon
In the OMG, the subgoal is selected by choosing the state within the future H steps that either maximizes or minimizes the value function V(s,g). To explore the impact different subgoal selection strategies, we introduced three alternatives: random selection within the H steps (OMG- random), selecting the first step as the subgoal (OMG-1s), and selecting the third step as the subgoal (OMG-3s). The results, presented in Figure 6(b) suggest that the choice of subgoal selection strategy significantly affects performance, with OMG's strategy leading to more effective training compared to the alternatives. We also observe that the subgoal often remains constant over consecutive time
steps for OMG-supervised. Further details can be found Appendix D
We further investigate our design choice on the subgoal selection for the policy. During the policy update, Equation (8) (i.e., g) utilized. As Pv pre-trained and fixed during the update phase, remains stable. On the other hand, which represents the inferred subgoal when executing the policy, also stabilizes as the training steps increase. Thus, we choose a gradual transition of y from ğ to ÿ. which should help avoid instability during the training of the subgoal inference model. Here we perform the experiments in the foraging environment with different subgoal inputs for the policy, i.e., 9, 0.9.9 As shown in Figure 7(a) and Figure 7(b) OMG with g indeed shows faster and better convergence.
The parameter // denotes the horizon of the subgoal selector. The ablation experiment results are shown in Figure 7(c) and Figure 7dd] is observed that an appropriate horizon value is neither excessively high nor excessively low. When H = 1, it essentially equivalent to combining with QSS [9] and opponent modeling, which can interpreted another way action modeling. However, H is set too large, such as H 10, the agent may skip important states in the trajectory, leading to degradation performance. Therefore, selecting an appropriate value for H is crucial in achieving satisfactory results.
5.5 Inferred Subgoal Analysis
We analyze the predictive performance of the opponent model. In Figure 8(a) we plot the ratio of that an opponent's future trajectory passes through the opponent's subgoal state, termed subgoal hit ratio. The subgoal state reconstructed by the inferred subgoal ğ using the decoder of the subgoal prior model. The subgoal hit rate gradually improves during training, which indicates that

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OMG-conserV
step=1
step=5
step-
step=8
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stepm]
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(a) Hit ratio of subgoal state
(h) Illustration of inferred subgoal state
Figure 8: Subgoal analysis of OMG in Foraging. The subgoal hit rates for OMG-conservatiive and OMG-optimistic are shown in Figure [(a) In Figure [(b) the agent controls player 1 (white), and the opponent controls player (blue). The blue circle represents the state obtained through the reconstruction of the subgoal inferred by the agent. The figure illustrates the difference between OMG-conservatiiv and OMG-optimistic under the same initial state and opponent policy.
the subgoal- -based opponent modeling is able predict the future state of the opponent. OMG tends to predict the opponent's future state several steps ahead as the subgoal, rather than focusing solely on the next step. This kind of prediction requires validation over multiple steps, and the agent policy conditioned on the predicted subgoal may also influence the behavior of the opponent. These make challenging to verify the predicted subgoal. Consequently, the overall hit ratio remains at moderate level at the end of training. There is small gap between the subgoal hit rates of OMG-conservative and OMG-optimistic, which leads to a longer episode length for OMG-optimistic illustrated in Figure 8(b) The root cause lies in the differences in the subgoal selection between OMG-conservative and OMG-optimistic. More details can be found in Appendix B
than 2MG-conservativv
Conclusion and Limitation
In this paper, we introduce OMG, novel method for opponent modeling based subgoal inference. OMG is simple and efficient opponent modeling method and can be combined with various RI. algorithms. Unlike most opponent modeling methods, which primarily focus on predicting the opponent's actions, OMG focuses on modeling the opponent's subgoals. Specifically, it leverages the value function of the policy to guide the selection of subgoals, which yields two variants of OMG for cooperative and general-sum games, respectively. Empirical results demonstrate the remarkable performance achieved by OMG, as compared to baselines based on action modeling, and that OMG exhibits better generalization when cooperating with opponents with unknown policies. We analyze the subgoals obtained by the inference model, and the results show they closely correlate with the opponent's 's trajectory. The limitation of OMG it cannot handle open multi-agent systems where agents may enter and leave during the interaction. This is left for future work.
Acknowledgments
This work was supported by NSFC under Grant 62450001 and 62476008. The authors would like to thank the anonymous reviewers for their valuable comments and advice.
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A Analysis of (s,g)
In opponent modeling, we usually build (s, g) and (s, (s,a-)) by observing the opponent's action trajectories. We construct a tree to describe the trajectories of the opponent's action sequences, as shown in Figure 9
The non-leaf nodes and edges represent the state and opponent's 's action respectively. Without loss of generality, we simplify the problem by using a complete tree with the leaf node as goal. The length of the action sequences is k and the opponent action space is denoted as A. We compare the number of (s. a) and .) that can be observed via trajectories, and their sets are denoted as S. and Sg respectively. The sizes of S₂ and Sg as:
R-1
n
card(S Σ
Σ
nA
nA - nA
1=0 sES())
k-1 Σ
card(S,)
TI(s g))
1=0 $ES gEG
|G|
G
|G| + AA
+ n
k-1
nAA
--1
=|G|
where 8()) represents the set of all states of depth in the tree, - g means is reachable from s. n is the size of A. Let cord(S,) S card(S.). we get a bound over [G], as Equation (9). When the goal number of our method is within the bound, the number of expanded states can be significantly reduced, which means the RL algorithm learns faster than those methods based on action modeling.
nA T -
card(S S card(S.) |G|
n4A S|| k
k
(na - 1)
(m4)
k-1
g
g
Figure 9: Illustration of opponent's 's decision tree. Circles, edges, and squares represent state nodes, action, and goal nodes respectively.
When |G| is below n.A /k times the number of observed states, the goal-based opponent modeling method proves more advantageous compared to the methods based action modeling- Consequently, this criterion can be met by maintaining a relatively modest value for k. Due to our method favoring the adoption of extreme values as goal states, a limited quantity of such states exist. So, it is loosely bound of [G] for OMG.
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B Experiments settings
Multi-Agent Environments. Foraging environment 2 is an 8 x 8 gridworld with full observation, containing two players: the agent and the opponent. At the beginning of each round, the players and three foods are randomly generated in the environment. The goal of the agent is to collect all foods as quickly as possible. The agent can move in four directions or pick up the food. The agent must judge the opponent's target food as soon possible to avoid futile actions for the same food.
Predator-Prey 20 three-against-one multi-agent environment with a continuous space. Three predators coordinate to touch the prey, and all participants have full observation. The agent acts as one of the predators, and the opponents are the other two predators and the prey, which leads the non-stationarity of the environment from the agent's 's view despite not belonging to one camp. The agent aims to maximize its reward and therefore needs to collaborate with the other two predators to complete the encirelement and cut the prey's escape route.
SMAC 35 is high-dimensional partial observation complex environment for research in the field of collaborative MARL based on StarCraft II. The agent joins a set of opponents with unknown policies accomplish the task. The only way to accomplish the task is collaborate with the other agents. The agent's goal to complete the task with a group of opponents controlled by unknown policies.
Opponent. The autonomous agent is trained in multi-agent environment, where it interacts with the opponents controlled by a set of pre-trained policies. At the onset of each episode, the opponent's policy is selected randomly from the set. In the case of SMAC, the autonomous agent's 's index is also randomly determined. For Foraging, Seedator-Prey. and SMAC environments, D3QN, PPO, and QMIX used to train the opponents, respectively. All the opponents in the training set comprise 10 distinct policies.
In SMAC, the test set consists of 30 opponents with different policies, trained by the IQL, VDN 41. and QMIX [3) In 8m, the opponents are reorganized into three groups: homologues, homologues, and non-homologues. In 3s_vs__ _5_,,__z, the opponents falls into two groups: homologues and non-homologues, Here, homologue refers to the policy from the same algorithm with the same parameters, and non-homologue represents the policy from two different algorithms. The remaining agent is controlled by OMG or baseline algorithms.
When assessing the performance of the autonomous agent in the SMAC with a test set, these opponents in the are trained separately using IQL, VDN, and QMIX, with 10 instances for each training method. To illustrate the dissimilarity of the test opponent's s policies, we utilize set of identical states to acquire the action vectors of the policy in the test set. We visualize the action vectors, as demonstrated in Figure TO The figure shows the diversity of test set policies employed by the test opponents. The test results are averaged over 100 episodes of fine-tuning, with random seeds.
iql
iql
10
qmix vdn
qmix
vdn
(a) 8m
(b) 3s vs_ 52
Figure 10: The distribution of the opponent's policy for the test of generalization.
15

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Pre-train the subgoal's prior model. The subgoal's prior model pv(g)=") is a VAE that learns from of states that are collected while training opponents. The optimization objective of VsE
arg max (gls)
KL 9 (
(10)
w
The decoder Pw is also used to reconstruct the subgoal state, as discussed in Section 5.5
Hyperparameters. All hyperparameters listed in Table
Table 1: Hyperparameters
Q-based RI.
Foraging(D3QN)
SMAC(QL)
Policy-based RI.
Predator prey((POO)e)P)))))
hidden units activation
MLP[64, 32]
RNN[64, 64]
hidden units
MLP(64,
ReI.U
ReL.U
activation function
optimizer
Adam
RMSProp
optimizer
Adam
learning rate
0.005
0.0005
learning rate
0.0005
RL Algorithm
target update interval
100
200
of updates
10
epsilon epsilon epsilon anneal time
value discount
0.99
0.95
0.95
GAE parumeter
4500
50000
clip parameter
0.115
butch size
32
32
max grad norm
0.5
butfer size
5000
5000
hidden units
MLP(64, 32)
MLP(64. 32]
MLP(64, 32]
learning rate
0.001
0,001
0.001
subgoal horizon H
Opponent model
KI, weight Aq
0.001
0.001
0.001
0.001
start
0.5
0.5
0.5
anneal time
50000
50000
50000
The computational resources for the experiments are as follows: the CPU is Intel(R) Xeon(R) Platinum 8280 CPU @ 2.70GHz, and the GPU is A100-PCIE-40GB.
C Performance of CTDE agent in autonomous agent task
The motivation of this paper to address the autonomous agent through opponent modeling. The question is, can the CTDE agents be adapted to do tasks like autonomous agents? The two domain are fundamentally different, and the training method CTDE doesn't ''t work well in such situations because it hasn't it been exposed to variety of opponents during its training. We conducted tests in 8m where QMIX acts as the agent with opponents of test set.
Table 2: Test performance on 8m
opponent type 7 non-homologue
6 homologue
homologue
QMIX
21.6%
65.6%
61.0%
OMG-optim 70.5%
86.8%
90.2%
This training paradigm employed by QMIX leads to lack of generalization for different opponents. Using the same training methodology for QMIX OMG leads to degradation in IQL,which already serves as one of the existing baselines. The test results indicate that opponents trained using different methods and seeds not homogeneous, which poses challenges for cooperation.
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D Sy selection frequency
In Equation 66 and Equation 7 subgoals are selected from N,
{ 1 S k S H). where N," a sliding window. If the value monotonic along the trajectory, a possible case that different subgoals are chosen at each step. We used 100 trajectories and counted the selection frequency within the trajectory, as shown Table
Table 3: The proportion of each s in NY
k
2
3
4
proportion 35.4% 20.0%
22.8%
19.3%
2.5%
The results suggest that in multi-agent settings, characterized by cooperative and competitive interac- tions among agents, the value function displays multiple peaks along the trajectory. Additionally, the selected subgoals exhibit a certain level continuity over several steps.
E Details for Inferred Subgoal Analysis
Subgoal hit ratio. Define the opponent's trajectory sequence from t 0 to T as T (So, $1..... ..... ST) and the agent's prediction from time to
T = (Su, 81 ... ST 1).
Let T; (8;, Si+1..... $T) represent the opponent's 's trajectory from step onward.
The subgoal hit ratio is calculated as follows:
{& 8, E Tr, ................................ T 1)1
subgoal hit ratio
[
where {&s & Tr, 0, 1, represents the of predicted states that are also present in the opponent's 's future trajectory starting from the current time step t.
For example, the opponent's trajectory is T (51, $2, 83, 84, 55). For each time step, the relevant opponent trajectory is: To (51, $2, 83, 94, 85). Ti (52, $3, 84, $5), To = (53, 84, st). Ta = (84, (5), The agent's 's predictions are = (sa, 81, 85, 85). The matched predicted states are {#3. 85).
Thus, the hit ratio is calculated as:
188, 8531 |{ [1, S2, 83, 84, 85
2 5
subgoal hit ratio
0.4
The complete trajectory of the example in Figure 8(b) is shown below:
OMG-consery
(b) OMG-optim
Figure 11: Illustration of inferred subgoal state
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OMG based on PPO
Algorithm 2 OMG based on PPO
Preparation:
2: Interact with V opponents to collect and train the prior model fv
3: Initialize subgoal inference model parameters and
4: Initialize policy parameters 8 and value function parameters yp
5: for k=0,1,2.... do
6: Interaction phase
7: Observe state & and last opponent's action a -i
8: Infer the subgoal by subgoal inference model (o())))
9:
Choose action a by T62 (-1s. 9)
10:
Store experience (s, .r) in buffer Dj:
11:
Update phase
12:
Calculate prior subgoal by Equation (6 or Equation 7
13:
Calculate subgoal by Equation
14:
Update policy parameters
5k+1 arg max
1 DAIT
Σ
Σ
min (T((ls)))
A (st, Ate (s,, (11)
T5. (at (t)
TED
15:
Update value parameters by
Pk++1 arg min
Σ
Σ
(Vo(st) -Ri)²
(12)
|Da/T
TED t=
16: Update inference model ds and pe by Equation 5
17:
end for
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NeurIPS Paper Checklist
1. Claims
Question: Do the main claims made in the abstract and introduction accurately reflect the paper's contributions and scope?
Answer: [Yes]
Justification: The abstract and introduction accurately summarize the paper's contributions by outlining the OMG method, its application to cooperative and general-sum games, and its superior performance.
Guidelines:
The answer NA means that the abstract and introduction do not include the claims made paper.
The abstract and/or introduction should clearly state the claims made, including the contributions made in the paper and important assumptions and limitations. A No
NA answer to this question will not be perceived well by the reviewers.
The claims made should match theoretical and experimental results, and reflect how much the results can be expected to generalize to other settings.
is fine to include aspirational goals as motivation as long as is clear that these goals not attained by the paper.
2. Limitations
Question: Does the paper discuss the limitations of the work performed by the authors?
Answer: [Yes]
Justification:
See Section
Guidelines:
The answer NA means that the paper has limitation while the answer No means that the paper has limitations, but those are not discussed in the paper.
The authors are encouraged to create a separate "Limitations" section in their paper.
The paper should point out any strong assumptions and how robust the results are to violations of these assumptions (c.g.. independence assumptions, noiseless settings, model sell-specfiiaatinn asymptotic approximations only holding locally). ). The authors should reflect on how these assumptions might be violated in practice and what the implications would be.
The authors should reflect the scope of the claims made, e.g. if the approach was only tested on few datasets or with few runs. In general, empirical results often depend on implicit assumptions, which should be articulated.
The authors should reflect on the factors that influence the performance of the approach. For example, facial recognition algorithm may perform poorly when image resolution low or images are taken in low lighting. Or speech-to-tex, system might not be used reliably to provide closed captions for online lectures because it fails handle technical jargon.
The authors should discuss the computational efficiency of the proposed algorithms and how they scale with dataset size.
If applicable, the authors should discuss possible limitations of their approach to address problems of privacy and faimesss.
While the authors might fear that complete honesty about limitations might be used by reviewers as grounds for rejection, a worse outcome might be that reviewers discover limitations that aren't 't acknowledged in the paper. The authors should use their best judgment and recognize that individual actions in favor of transparency play an impor- tant role in developing norms that preserve the integrity of the community, Reviewers will be specifically instructed to not penalize honesty concerning limitations.
3. Theory Assumptions and Proofs
Question: For each theoretical result, does the paper provide the full set of assumptions and complete (and correct) proof?
19

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Answer: [NA]
Justification: This paper does not have strict theoretical results. Appendix example analysis, shedding light the insights of the method presented in this paper, though it has not yet advanced to the theoretical level.
Guidelines:
The answer NA means that the paper does not include theoretical results.
All the theorems, formulas, and proofs in the paper should be numbered and cross- referenced.
All assumptions should be clearly stated or referenced the statement of any theorems.
The proofs can either appear the main paper or the supplemental material, but they appear in the supplemental material, the authors are encouraged to provide short proof sketch to provide intuition.
Inversely, any informal proof provided in the core of the paper should be complemented by formal proof's provided in appendix supplemental material.
Theorems and Lemmas that the proof relies upon should be properly referenced.
4. Experimental Result Reproducibility
Does the paper fully disclose all the information needed to reproduce the main ex- perimental results of the paper to the extent that it affects the main claims and/or conclusions the paper (regardless of whether the code and data are provided or not)?
Question:
Answer: [Yes]
Justification: The algorithm is described in detail as Algorithm| I and Algorithm 2 The code is provided in the supplemental material, and all hyperparameters and environment Settings are listed in the Appendix B
Guidelines:
The answer NA means that the paper does not include experiments.
If the paper includes experiments, No answer to this question will not be perceived well by the reviewers: Making the paper reproducible is important, regardless of whether the code and data are provided or not.
If the contribution is dataset and/or model, the authors should describe the steps taken to make their results reproducible or verifiable.
Depending on the contribution, reproducibility can be accomplished in various ways. For example, if the contribution is novel architecture, describing the architecture fully might suffice, or if the contribution is specific model and empirical evaluation, it may be necessary to either make possible for others to replicate the model with the same dataset, or provide access to the model. In general. releasing code and data is often one good way to accomplish this, but reproducibility can also be provided via detailed instructions for how to replicate the results, access to a hosted model (e.g.. in the case of large language model), releasing of a model checkpoint, or other means that are appropriate to the research performed.
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5. Open access to data and code
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Reviews:
[{"review_id": "2Wfi6bFWM0", "reviewer": "Reviewer_gEZB", "summary": "This paper introduces a multi-agent reinforcement learning algorithm focused on opponent modelling through subgoal inference, termed Opponent Modelling based on Subgoal Inference (OMG). Unlike traditional models that predict immediate actions of opponents, OMG leverages historical trajectories to infer an opponent's future subgoals. This method is designed to enhance generalisation across various unseen opponent policies and includes distinct mechanisms for cooperative and general-sum games. The authors report that their approach outperforms traditional action prediction models in several multi-agent benchmarks.", "questions": "1. Could the authors provide more insight into how the subgoal predictor's performance might degrade or improve when scaling to environments with significantly more complex or numerous agents?\n2. Are there specific types of multi-agent environments where OMG might not perform as expected? What limitations in the model's assumptions should be considered?\n3. How does the model handle highly dynamic environments where the opponent's strategies evolve more rapidly than the model's training updates?\n4. Please see weaknesses.", "limitations": "While the authors have discussed the technical validation of their model, there could be more emphasis on practical limitations, such as computational overhead and real-time applicability in fast-paced environments.", "rating": 6, "confidence": 4, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "1. The approach of predicting subgoals instead of immediate actions may lead to more robust multi-agent systems. Predicting an opponent's short-term actions tends to provide limited information compared to understanding their long-term strategies.\n2. The paper is well-structured, with a clear exposition of the problem, detailed methodology, and coherent discussion of results. Diagrams and formulas are appropriately used to aid understanding.\n3. By focusing on subgoals, OMG potentially offers a more scalable and generalizable approach to opponent modelling in multi-agent systems, which could be beneficial for complex scenarios.", "weaknesses": "1. “The subgoal prior model, denoted as $p_{\\psi}$, is a pre-trained variational autoencoder (VAE) using the states previously collected in the environment”: What policy was used to collect these states to pre-train the prior model? This policy will have a huge impact on the coverage of the state space, and hence the subgoal inference model and final policy of OMG.\n\n2. I have concerns about the generalizability and scalability of this approach. The authors test their approach on SMAC as a complex domain with one easy map (8m) and one medium map (3s_vs_5z). A number of SMAC maps have been shown to be solvable by independent learning methods such as IQL [1] and IPPO [2]. Can the authors showcase performance on hard SMAC maps such as 6h_vs_8z, corridor, 27m_vs_30m which requires learning more complex strategies and have a higher number of agents?\n\n3. Experimental Concerns:\n\n    3a. Why do the authors use different baselines for each environment i.e. D3QN, PPO, and IQL for Foraging, Predator-Prey, and SMAC respectively? Each of these baselines have been used for these environments. [4]\n\n    3b. What variant of PPO was used for the Predator-Prey environment? Both IPPO [2] with individual agent critics and MAPPO [3] with centralised critics have shown to exhibit strong performance in a lot of cooperative benchmarks including predator-prey.\n\n    3c. It would be helpful to assess the impact of the approach if the authors can compare their approach to state-of-the-art CTDE techniques in MARL i.e. QMIX.\n\n\n[1] QMIX: Monotonic Value Function Factorisation for Deep Multi-Agent Reinforcement Learning\n\n[2] Is Independent Learning All You Need in the StarCraft Multi-Agent Challenge?\n\n[3] The Surprising Effectiveness of PPO in Cooperative, Multi-Agent Games\n\n[4] Benchmarking Multi-Agent Deep Reinforcement Learning Algorithms in Cooperative Tasks", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "Thank you for acknowledging our novel contributions as well as raising valuable questions.\n\n> ''The subgoal prior model, denoted as $p_\\psi$, is a pre-trained variational autoencoder (VAE) using the states previously collected in the environment'': What policy was used to collect these states to pre-train the prior model? This policy will have a huge impact on the coverage of the state space, and hence the subgoal inference model and final policy of OMG.\n\nTraining OMG requires a set of policies as the training set. During the preparation of the training set, states are collected to train the prior model. The policies used in the training set are described in Appendix B, lines 494-499. As you noted, $p_\\psi$, serving as an encoder, must cover the state space as thoroughly as possible. However, it does not limit the policies used to collect states, allowing for an expanded range of state collection in practice.\n\n> I have concerns about the generalizability and scalability of this approach. The authors test their approach on SMAC as a complex domain with one easy map (8m) and one medium map (3s_vs_5z). A number of SMAC maps have been shown to be solvable by independent learning methods such as IQL [1] and IPPO [2]. Can the authors showcase performance on hard SMAC maps such as 6h_vs_8z, corridor, 27m_vs_30m which requires learning more complex strategies and have a higher number of agents?\n\nWe tested on 6h_vs_8z, and both QMIX and our method (OMG-optim + 5 QMIX agent) had a win rate of 0%.\n|   | QMIX | OMG-optim + 5 homologue |\n|:-----:|:-----:|:-----:|\n| win rate | 0.0% | 0.0% |\n\nThe ability to predict an opponent's actions or subgoals is not the only factor that determines performance, especially in scenarios requiring close cooperation. We are testing on 27m_vs_30m and will provide the results later. This may be challenging due to the persistent scalability issues in opponent modeling.\n\n> 3a. Why do the authors use different baselines for each environment i.e. D3QN, PPO, and IQL for Foraging, Predator-Prey, and SMAC respectively? Each of these baselines have been used for these environments. [4]\n\nThe core of OMG is opponent modeling method, which does not restrict the type of underlying RL method. Therefore, we followed the original environment's setup.\n\n> 3b. What variant of PPO was used for the Predator-Prey environment? Both IPPO [2] with individual agent critics and MAPPO [3] with centralised critics have shown to exhibit strong performance in a lot of cooperative benchmarks including predator-prey.\n\nWe used IPPO. The centralized critics are not applicable to the setup of this study. Because, the motivation of this paper is to address the autonomous agent through opponent modeling, rather than training a group of agents for some task.\n\n> 3c. It would be helpful to assess the impact of the approach if the authors can compare their approach to state-of-the-art CTDE techniques in MARL i.e. QMIX.\n\nWe has conducted tests where QMIX acts as the agent with opponents of test set in **Appendix C**.\n\nThe training paradigm employed by QMIX leads to a lack of generalization for different opponents. Using the same training methodology for QMIX as OMG leads to a degradation in IQL, which already serves as one of the existing baselines. The test results indicate that opponents trained using different methods and seeds are not homogeneous, which poses challenges for cooperation.\n\n> Could the authors provide more insight into how the subgoal predictor's performance might degrade or improve when scaling to environments with significantly more complex or numerous agents?\n\nWhen modeling opponents, the difficulty of prediction usually escalates in environments with more complex or numerous agents, as the prediction space expands. From a scalability standpoint, OMG offers certain advantages over traditional action prediction methods. For example, if the state space of the environment excludes agent information, OMG's prediction space does not significantly increase with the number of agents.\n\n> Are there specific types of multi-agent environments where OMG might not perform as expected? What limitations in the model's assumptions should be considered?\n\nWe believe it is essential for opponents in the environment to have clear goals. An opponent with a purposeless, random policy is challenging to model, even though it might not directly impact the agent's rewards.\n\n> How does the model handle highly dynamic environments where the opponent's strategies evolve more rapidly than the model's training updates?\n\nOMG does not account for scenarios where opponents rapidly evolve during interactions. Addressing such situations requires incorporating planning ideas as discussed in [1, 2], which is left for future work. Currently, OMG addresses this by ensuring that the training set includes a diverse range of opponent policies, allowing it to generalize well even when opponents rapidly evolve during testing.\n\n[1] Zhi-Xuan T, Mann J, Silver T, Tenenbaum J, Mansinghka V. Online bayesian goal inference for boundedly rational planning agents. Advances in neural information processing systems. 2020;33:19238-50\n\n[2] Xiaopeng Yu, Jiechuan Jiang, Wanpeng Zhang, Haobin Jiang, and Zongqing Lu. Model-based opponent modeling. Advances in Neural Information Processing Systems, 35:28208–28221, 2022.", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "eCpVuOnouO", "reviewer": "Reviewer_fQcX", "summary": "The paper is positioned within the ad-hoc teamwork problem in multi-agent systems, where an agent faces partners it has not seen before in training, and must learn to cooperate with them towards performing a task that benefits from cooperation. Authors deal with a specific requirement of ad-hoc teamwork that is opponent modelling: an agent's ability to model other agents in the system. They propose to model other agents at the level of their subgoals, inferred from the observed trajectories of interaction. They propose to learn a Q-function that also takes the inferred opponent sub-goal as input, thus making the policy of the protagonist agent conditioned on the sub-goal of the opponent. The empirical results seem to suggest minor improvements over previous opponent modelling works.", "questions": "Q1: \"_However, focusing on the opponent’s action\nis shortsighted, which also constrains the adaptability to unknown opponents in complex tasks_\"  \n\nWhat do you mean by \"shortsighted\"? How does that _constrain_ the adaptability? These are strong statements but are not concretised at all.\n\nQ2: \"_...bridge the information gap between agents_\"\n\nThis concept of _information gap_ appeared out of nowhere. It is not explained either. What does this even mean? It needs to be clarified.\n\nQ3: \"_Autonomous agents, different from those jointly trained, can act autonomously in complex and dynamic environments..._\"\n\nYou seem to be conflating autonomy with decentralized training or being self-interested here. The definition of autonomy does not preclude centralised training. I can have a set of autonomous agents train with privileged information, yet deploy them to act autonomously. \n\nQ4: \"_Although a lot of the existing methods concentrate on modeling the opponent’s actions, we argue that such an approach is short-sighted, pedantical, and highly complex._\"\n\nAgain, lots of sweeping and strong statements with no backing or clarification. What does short-sighted, pedantical, and highly complex mean? This does not sound professional or scientific. If you are going to actually complain about an entire line of literature, you need to make your statement more concrete. \n\nQ5: \"_Generally, modeling an opponent’s actions just predicts what it will do at the next step. Intuitively, it is more beneficial for the agent to make decisions if it knows the situation of the opponent several steps ahead_\"\n\nThis statement seems to ignore the trajectory prediction literature entirely, and tries to get away with it by saying \"generally\". \n\nQ6: \"_Other methods that claim to predict the opponent’s goal [28 , 29], but without explicitly making a connection to the opponent’s goal..._\" \n\nWhat does this even mean? Also, see the inverse planning / goal recognition works cited in Weaknesses and their references/citations for works that predict goals explicitly.\n\nQ7: \"_Unlike these methods, in this paper, we consider the most common..._\"\n\nI would argue that the setting where other _autonomous_ agents are also learning and adapting to our agent is the more common setting, and the fixed opponent policy is a big simplification of it. This can be justified in certain cases, but it certainly is not the _most common,_ except that it is more common in literature because it is simpler. But if the harder and more realistic problem is already being tackled, I do not see why this point is a plus. \n\nQ8: The $\\pi^o, a^o$ notation is confusing. I would recommend using the pre-established notational norms in game theory / MARL, $\\pi^{-i} , a^{-i}$ for all agents except $i$.\n\nQ9: \"_Opponent modeling typically predicts the actions of other agents to address the non-stationary problem_.\" \n\nAt this point, I am a little confused. You have said \"_Unlike these methods, in this paper, we consider the most common setting where opponents have unseen, diverse, but **fixed policies** during test_.\" So the opponents have fixed policies during test. Then there is absolutely no non-stationarity during test time. In fact, since $\\pi^o$ is fixed within a test episode, the problem the agent is facing in test time is in fact an MDP. So you are only dealing with the setting where at each episode the agent might be facing a new MDP. How is this different from online single-agent reinforcement learning then?", "limitations": "Yes.", "rating": 5, "confidence": 4, "soundness": 3, "presentation": 3, "contribution": 2, "strengths": "**Originality**\n- I do not believe there is much strength in terms of originality.\n\n**Quality**\n- The submission seems technically sound to me _except_ for the definition of a sub-goal. A sub-goal is defined as a feature embedding of a future state. This is not sound to me (see Weaknesses).\n\n**Clarity**\n- The clarity of the submission is slightly above average.\n\n**General Comments**\nAs someone from this particular niche, I believe the paper is studying an important problem. Overall, I believe their approach of augmenting state-spaces with inferred information about the opponents is perhaps an under-explored direction.", "weaknesses": "**Originality**\n- I do not believe that goal and sub-goal inference for modelling agents is original. The paper is missing an entire line of research in their related works here, namely the inverse planning literature. This community has been studying inferring goals and sub-goals from trajectories through probabilistic modelling of other agents for a long time now (e.g. see [1,2] as a starting point and follow the thread of references and citations).  In addition, inferring and modelling goals of others is not original also in the ad-hoc teamwork literature (see [3,4]). Others also considered goal recognition between agents actively [5]. These are only some of the papers in this line of work, as there are many more. I am surprised to see none of these works are cited. I would like to see a discussion on what is the novelty/originality left after this literature is accounted for. Conditioning the Q-function on the goal of other is also not an original idea, but this is not the main claim any way.\n\nAdditionally, the problem of learning to cooperate with previously unseen teammates has been defined and named as \"ad-hoc teamwork\" in 2010 [6]. Since it is literally the problem setting of the authors, I am surprised there is no mention of this and the original paper is not cited.\n\n[1] Zhi-Xuan T, Mann J, Silver T, Tenenbaum J, Mansinghka V. Online bayesian goal inference for boundedly rational planning agents. Advances in neural information processing systems. 2020;33:19238-50\n\n[2] Ying L, Zhi-Xuan T, Mansinghka V, Tenenbaum JB. Inferring the goals of communicating agents from actions and instructions. InProceedings of the AAAI Symposium Series 2023 (Vol. 2, No. 1, pp. 26-33).\n\n[3] Melo FS, Sardinha A. Ad hoc teamwork by learning teammates’ task. Autonomous Agents and Multi-Agent Systems. 2016 Mar;30:175-219.\n\n[4] Chen S, Andrejczuk E, Irissappane AA, Zhang J. ATSIS: achieving the ad hoc teamwork by sub-task inference and selection. InProceedings of the 28th International Joint Conference on Artificial Intelligence 2019 Aug 10 (pp. 172-179).\n\n[5] Shvo M, McIlraith SA. Active goal recognition. InProceedings of the AAAI Conference on Artificial Intelligence 2020 Apr 3 (Vol. 34, No. 06, pp. 9957-9966).\n\n[6] Stone P, Kaminka G, Kraus S, Rosenschein J. Ad hoc autonomous agent teams: Collaboration without pre-coordination. InProceedings of the AAAI Conference on Artificial Intelligence 2010 Jul 5 (Vol. 24, No. 1, pp. 1504-1509).\n\n**Quality**\n- The experimental section only compares to two relatively simple opponent modelling works LIAM and \"Naive OM\". However, the authors for instance literally cite the \"Machine Theory of Mind\" paper and the \"Modelling others using oneself in multi-agent reinforcement learning\" in related works. Surely these are the closest competitors to their method. Additionally, some of the papers listed above under originality are also close competitors. I believe you need more than two methods in opponent modelling baselines. Especially the two methods compared are by no means considered the state-of-the-art.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "## Part Ⅰ\n\nThank you for valuable comments. Below is a detailed response to your question, addressing each point individually.\n\n> I do not believe that goal and sub-goal inference for modelling agents is original. The paper is missing an entire line of research in their related works here, namely the inverse planning literature. This community has been studying inferring goals and sub-goals from trajectories through probabilistic modelling of other agents for a long time now (e.g. see [1,2] as a starting point and follow the thread of references and citations). In addition, inferring and modelling goals of others is not original also in the ad-hoc teamwork literature (see [3,4]). Others also considered goal recognition between agents actively [5]. These are only some of the papers in this line of work, as there are many more. I am surprised to see none of these works are cited. I would like to see a discussion on what is the novelty/originality left after this literature is accounted for. Conditioning the Q-function on the goal of other is also not an original idea, but this is not the main claim any way. Additionally, the problem of learning to cooperate with previously unseen teammates has been defined and named as \"ad-hoc teamwork\" in 2010 [6]. Since it is literally the problem setting of the authors, I am surprised there is no mention of this and the original paper is not cited.\n\nWe will add more relevant references to enhance the related works section. Below, we explain the differences between our work and the references you mentioned to highlight our contributions and originality.\n\nOur method represents an innovation in the field of opponent modeling. As described, OMG is applicable to both cooperative games and general-sum games, and is not limited to \"ad-hoc teamwork\" [3,4,6]. OMG emphasizes methodological innovation rather than focusing solely on the ability to solve specific tasks.\n\nAdditionally, inferring goals is a straightforward concept and is commonly addressed in numerous papers [5, 7, 8, 9]. However, in the context of opponent modeling for autonomous agents, this method is novel. Unlike the method in [2], which requires agents to communicate with each other, our setting involves autonomous agents that cannot communicate with other agents. Model-based methods [1] require constructing an environmental model and involve extensive computation for planning during execution. This approach differs from the model-free method adopted in this work.\n\n> The experimental section only compares to two relatively simple opponent modelling works LIAM and \"Naive OM\". However, the authors for instance literally cite the \"Machine Theory of Mind\" paper and the \"Modelling others using oneself in multi-agent reinforcement learning\" in related works. Surely these are the closest competitors to their method. Additionally, some of the papers listed above under originality are also close competitors. I believe you need more than two methods in opponent modelling baselines. Especially the two methods compared are by no means considered the state-of-the-art.\n\nOMG differs from traditional action prediction methods in opponent modeling by introducing a new approach based on subgoal inference. Therefore, we selected related methods as baselines. To the best of our knowledge, we have compared state-of-the-art (SOTA) methods in this domain. Below, we will explain why certain methods were not included as baselines.\n\n[1] describes a planning algorithm using \"Sequential Inverse Plan Search,\" which is fundamentally different from the model-free algorithm used in this paper. The only similarity is the concept of \"goal inference.\" In [2], agents are able to communicate with each other, unlike our setting with autonomous agents that cannot communicate. References [3, 4, 6] focus on ad-hoc teamwork. The method in [3] does not use deep learning and is difficult to apply to complex environments like SMAC. [4] uses Goal-Conditioned RL (GCRL) and requires goals to be manually defined, whereas OMG does not. Additionally, goal-based reward shaping limits [4] to cooperative tasks. The problem addressed in [5] is active goal recognition, which is quite different from our approach of optimizing policies through opponent modeling. We have conducted a comprehensive survey of related work and compared all relevant baselines under fair conditions.\n\n\n[1] Zhi-Xuan T, Mann J, Silver T, Tenenbaum J, Mansinghka V. Online bayesian goal inference for boundedly rational planning agents. Advances in neural information processing systems. 2020;33:19238-50\n\n[2] Ying L, Zhi-Xuan T, Mansinghka V, Tenenbaum JB. Inferring the goals of communicating agents from actions and instructions. InProceedings of the AAAI Symposium Series 2023 (Vol. 2, No. 1, pp. 26-33).\n\n[3] Melo FS, Sardinha A. Ad hoc teamwork by learning teammates’ task. Autonomous Agents and Multi-Agent Systems. 2016 Mar;30:175-219.\n\n[4] Chen S, Andrejczuk E, Irissappane AA, Zhang J. ATSIS: achieving the ad hoc teamwork by sub-task inference and selection. InProceedings of the 28th International Joint Conference on Artificial Intelligence 2019 Aug 10 (pp. 172-179).\n\n[5] Shvo M, McIlraith SA. Active goal recognition. In Proceedings of the AAAI Conference on Artificial Intelligence 2020 Apr 3 (Vol. 34, No. 06, pp. 9957-9966).\n\n[6] Stone P, Kaminka G, Kraus S, Rosenschein J. Ad hoc autonomous agent teams: Collaboration without pre-coordination. AAAI 2010.\n\n[7] Silviu Pitis, Harris Chan, Stephen Zhao, Bradly Stadie, and Jimmy Ba. Maximum entropy gain exploration for long horizon multi-goal reinforcement learning. ICML, 2020.\n\n[8] Suraj Nair, Silvio Savarese, and Chelsea Finn. Goal-aware prediction: Learning to model what matters. ICML, 2020.\n\n[9] Menghui Zhu, Minghuan Liu, Jian Shen, Zhicheng Zhang, Sheng Chen, Weinan Zhang, Deheng Ye, Yong Yu, Qiang Fu, and Wei Yang. Mapgo: Modelassisted policy optimization for goal-oriented tasks. IJCAI, 2021.", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "KK7x8X9hmt", "reviewer": "Reviewer_FFHE", "summary": "For cooperative games and general-sum games, this paper proposes opponent modeling by inferring an opponent’s subgoals, rather than inferring actions. They empirically verify that this leads to either similar or better scores over baselines in Foraging (discrete grid game), Predator-Pray (continuous game), and SMAC (high dimensional), as well as a reduction in required timesteps per episode to reach comparable scores to baseline.", "questions": "- L152 — missing word?  “will reach the same ” → “will reach the same state”\n- L159-160 — confusing sentence: “...resulting from the tuple (s, a^o, a) is more than numerous than (s,g,a) in the Q-table”\n- L190 — confusing preposition: “state as…” → “state of”? \n- L204 and L206-207 — both sentences here claim seemingly contradictory statements: “...adopting an optimistic strategy akin to the minimax strategy, which applies to cooperative games” seems to contradict the following statement “...leading to a conservative strategy similar to the minimax strategy, which is commonly used for general-sum games”. Are these both similar to minimax? \n- Section 4.2: Subgoal Selector. This section is a bit hard to follow the reasoning for Eq. 6 and Eq. 7 for OMG-optimistic and OMG-conservative, even after referring to 4.1 Can you clarify in this section why you provide these two distinct manners for subgoal selection? \n- Section 5, Figure 5 — It is not immediately clear what the X-axis is representing. The numbers in front of “non-homologue” and “homologue” do not have context (they are only clear from reading the Appendix). Can you add a sentence to the description of the Figure? Can you expand on the sentence: “The X-axis represents the opponent’s policies, and “homologue” refers to the policy learned by the same algorithm, while “non-homologue” represents different ones”? \n- L294 — possible typo: “interrupted” → “interpreted”\n- Figure 7b — OMG-conserv shows step 1, 5, 6, and 8; OMG-optim shows steps 1, 5, 8, 10. Is there a reason the steps are not matched? (i.e both showing 1,5,6,8 or 1,5,8,10) \n- L299-300 — the wording of the definition for hit ratio is a bit unclear. Is this essentially the ratio of predicted opponent trajectory to actual opponent trajectory? \n- Section 5.5: How do you determine the hit ratio if the subgoal is several steps ahead of the current state? For example, if a predicted subgoal is 3 steps north, the opponent could reach the subgoal in 3 steps or more steps. How many steps can an opponent take between the subgoal prediction state in order for it to still count as a hit? \n- L479 — Typo: “ovservation” → “observation” \n- L504 — Typo: “remained” → “remaining”", "limitations": "Yes.", "rating": 7, "confidence": 3, "soundness": 4, "presentation": 3, "contribution": 3, "strengths": "- The paper is well organized, provides ample context and prior research, and solid empirical evidence to prove its method. \n- The idea of predicting subgoals rather than actions is rather intuitive, and the authors are clear in its formalization. \n- The method is novel. \n- The paper is fair and thorough in its comparison to baselines. Environments are diverse (discrete, continuous, high dimensional), baseline+OMG share the same neural network architecture, tests are run across 5 seeds and plots provide mean+standard deviation. \n- A dedicated ablation studies section clarifies the reasoning behind the choice of VAE, horizon, and subgoal selection. \n- Code is provided in supplementary material and will be open sourced upon acceptance", "weaknesses": "- Improvements over scores in baselines are minor in Foraging. The main difference between the baselines appears to be in the reduction of the episode steps. It would be interesting to see if there is a reduction in the average time steps towards the end of training in Predator-Prey. \n- Minor typos and clarifications requested in Questions.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "Thank you for acknowledging our novel contributions as well as raising valuable questions.\n\n> Improvements over scores in baselines are minor in Foraging. The main difference between the baselines appears to be in the reduction of the episode steps. It would be interesting to see if there is a reduction in the average time steps towards the end of training in Predator-Prey.\n\nThe Predator-Prey has a fixed episode length. The score represents the number of times the predators touch the prey. Therefore, this result already reflects a reduction in the average touch time.\n\n> L152 — missing word? “will reach the same ” → “will reach the same state”\n\nThank you for your correction. In this paper, goal $g$ represents a feature embedding of a future state. Therefore it is more accurate to use \"will reach the same feature embedding\" and we will fix it.\n\n> L159-160 — confusing sentence: “...resulting from the tuple (s, a^o, a) is more than numerous than (s,g,a) in the Q-table”\n\nIn the example shown in Figure 3, $(\\mathcal{A} = \\mathcal{A}^o = \\{ \\text{none}, \\uparrow, \\downarrow, \\leftarrow, \\rightarrow \\})$ and $(\\mathcal{G} = \\{D_1, D_2\\})$. In the Q-table, the number of cells for $(s, g, a)$ is $(10 \\cdot |S|)$, which is fewer than the number of cells for $(s, a^o, a)$.\n\n> L190 — confusing preposition: “state as…” → “state of”?\n\nThis sentence implies that the selected state is being treated or used as a subgoal. Emphasizes the role or function of the state in the context of the model. We modify it in the revision to disambiguate.\n\n> L204 and L206-207 — both sentences here claim seemingly contradictory statements: “...adopting an optimistic strategy akin to the minimax strategy, which applies to cooperative games” seems to contradict the following statement “...leading to a conservative strategy similar to the minimax strategy, which is commonly used for general-sum games”. Are these both similar to minimax?\n\nIn Line 204, the maximax strategy is used, while Line 206 employs the minimax strategy. These two strategies are different.\n\n> Section 4.2: Subgoal Selector. This section is a bit hard to follow the reasoning for Eq. 6 and Eq. 7 for OMG-optimistic and OMG-conservative, even after referring to 4.1 Can you clarify in this section why you provide these two distinct manners for subgoal selection?\n\nThe maximax strategy aims to maximize the maximum possible gain. It is an optimistic approach that focuses on the best possible outcome. The formula is as follows:\n\n$a = \\arg\\max_{a_i \\in \\mathcal{A}} \\left(\\max_{a_o \\in A_o} (P(a_i, a_o)) \\right)$.\n\nThe minimax strategy focuses on maximize the minimum gain. The formula is as follows:\n\n$a = \\arg\\max_{a_i \\in \\mathcal{A}} \\left(\\min_{a_o \\in A_o} (P(a_i, a_o)) \\right)$\n\nIn Eq.6 corresponds to the inner \"max\" in the maximax strategy, and Eq.7 corresponds to the inner \"min\" in the minimax strategy. RL corresponds to the outer \"max\" of both.\n\n> Figure 7b — OMG-conserv shows step 1, 5, 6, and 8; OMG-optim shows steps 1, 5, 8, 10. Is there a reason the steps are not matched? (i.e both showing 1,5,6,8 or 1,5,8,10)\n\nThe trajectories formed by the two algorithms have different lengths and cannot be matched exactly. We will release the full trace instead of the key steps in the appendix.\n\n> L299-300 — the wording of the definition for hit ratio is a bit unclear. Is this essentially the ratio of predicted opponent trajectory to actual opponent trajectory?\n\n> Section 5.5: How do you determine the hit ratio if the subgoal is several steps ahead of the current state? For example, if a predicted subgoal is 3 steps north, the opponent could reach the subgoal in 3 steps or more steps. How many steps can an opponent take between the subgoal prediction state in order for it to still count as a hit?\n\nFor example, the opponent’s trajectory sequence from $ t=0 $ to $ t=4 $ is $(s_1, s_2, s_3, s_4, s_5)$. The agent's prediction from $ t=0 $ to $ t=3 $ is $(s_3, s_1, s_5, s_5)$. The hit ratio is calculated as $\\frac{|\\{s_3, s_5\\}|}{|\\{s_1, s_2, s_3, s_4, s_5\\}|} = 0.4$. The predicted $s_1$ at $ t=1 $ is not counted because $s_1$ is not present in the trajectory sequence from $t>=1$. We'll add a detailed explanation in the appendix.\n\n> Section 5, Figure 5 — It is not immediately clear what the X-axis is representing. The numbers in front of “non-homologue” and “homologue” do not have context (they are only clear from reading the Appendix). Can you add a sentence to the description of the Figure? Can you expand on the sentence: “The X-axis represents the opponent’s policies, and “homologue” refers to the policy learned by the same algorithm, while “non-homologue” represents different ones”?\n\n> L294 — possible typo: “interrupted” → “interpreted”\n\n> L479 — Typo: “ovservation” → “observation”\n\n> L504 — Typo: “remained” → “remaining”\n\nThank you for your suggestions and corrections. We will fix it in the revision.", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "seUv9NihLd", "reviewer": "Reviewer_FFHk", "summary": "The paper proposes an algorithm for learning policy in a multi-agent environment that predicts subgoal intents of other agents. In this way, the authors address the non-stationarity problem in multi-agent learning. Experiments in three environments show an advantage of the approach over baselines.", "questions": "What is the speed of training and inference of OMG compared to Naive OM and standard RL baselines (wall time)?", "limitations": "One limitation is mentioned in Section 6. Actually, I don't see why OMG cannot handle open systems. However, I'd add other limitations, such as: modeling subgoals instead of actions is much harder if the state space is much more complex than the action space (e.g., in video games). Additionally, predicting future states may be prohibitively challenging if the policy strongly depends on the opponent's moves (e.g., chess).\n\nThere is no potential negative societal impact of this work.", "rating": 6, "confidence": 3, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "- The proposed method is simple and interesting.\n\n- The paper is well-organized and mostly clear.\n\n- Pseudocode and data flow charts are helpful.", "weaknesses": "- Experiments: It's a bit disappointing that in most of the presented experiments, the confidence intervals of OMG and baselines generally overlap (except in the predator-prey environment). I understand that controlling a single agent makes it hard to jump from 10% to 90%. However, I suggest choosing environments that amplify the impact of a single agent. For instance, the 3s_vs_5z environment seems well-chosen (hence the highest advantage). In either case, increasing the number of trials to make confidence intervals tighter would also help.\n\n- The authors are sometimes overconfident in their claims. \"Obviously, the complexity and uncertainty of predicting the action sequence are much higher than the goal itself\" -- this is not always obvious. I agree that in some cases it is true, but there are also many domains where minor action changes lead to completely different states, resulting in much higher uncertainty in predicting subgoals. Instead of suggesting that OMG is always better, I recommend analyzing in which contexts OMG is better. Also, \"... the results show they closely correlate with the opponent's trajectory\" -- I acknowledge the reported 12-14% hit ratio, particularly given that the intents may change, but I'm not convinced that's enough evidence to claim \"closely correlated\".\n\n- Equations 6-7: It's confusing that g in V(s_t, g) is the opponent's subgoal, while the notation resembles the standard goal-conditioned value function. I suggest replacing it with V(s_t, g^o), similar to a^o, or using any other indication that it's the opponent's subgoal. Additionally, to analyze the impact of choosing either (6) or (7), you should include an ablation (even a single experiment with just the results provided) in which you compare to naive choices, such as a random state or a fixed-distance state (e.g., s_t+3). This is especially important given that in Appendix D you report that 80% of subgoals are <=3 steps.\n\nMinor comments:\n\n- l.139: Technically, by modeling the opponents' subgoals, you don't gain any new information because everything is computed from the observation.\n\n- l.148: Why is |G| finite? I think you didn't assume the finiteness of anything, including the action space.\n\n- l.154-157: This claim needs stronger support to be that general. The experiment you show here is an illustrative example, too small to frame the takeaway so broadly.\n\n- l.160: Why are there fewer subgoal tuples? I understand that both methods create exactly one datapoint for every step. If that's because of duplicates in the buffer, then this example may not be fully relevant (as in other environments, it is nearly impossible to repeat exactly the same state).\n\n- l.297: I'd also mention here which value of H you've chosen.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "Thanks for your valuable comments. As follows, we address your concerns in detail.\n\n> Experiments: It's a bit disappointing that in most of the presented experiments, the confidence intervals of OMG and baselines generally overlap (except in the predator-prey environment). I understand that controlling a single agent makes it hard to jump from 10% to 90%. However, I suggest choosing environments that amplify the impact of a single agent. For instance, the 3s_vs_5z environment seems well-chosen (hence the highest advantage). In either case, increasing the number of trials to make confidence intervals tighter would also help.\n\nWhile OMG does not show a significant advantage in the experiments, it maintains a modest but consistent edge. This is reasonable, considering that opponent-predicting ability is not the sole factor influencing performance.\n\nWe have increased the number of runs to 10 seeds for Predator-prey, and the result presents in the PDF file of \"global\" response.\n\n> Equations 6-7: It's confusing that g in V(s_t, g) is the opponent's subgoal, while the notation resembles the standard goal-conditioned value function. I suggest replacing it with V(s_t, g^o), similar to a^o, or using any other indication that it's the opponent's subgoal. Additionally, to analyze the impact of choosing either (6) or (7), you should include an ablation (even a single experiment with just the results provided) in which you compare to naive choices, such as a random state or a fixed-distance state (e.g., s_t+3). This is especially important given that in Appendix D you report that 80% of subgoals are <=3 steps.\n\nFollowing your suggestion, we have added ablation experiments. In these experiments, OMG-random, OMG-1s, and OMG-3s represent subgoals selected from the opponent's future states randomly, at the next step, and at three steps ahead, respectively. The results present in the PDF file of \"global\" response.\n\n> l.139: Technically, by modeling the opponents' subgoals, you don't gain any new information because everything is computed from the observation. l.148: Why is |G| finite? I think you didn't assume the finiteness of anything, including the action space.\n\nThank you for your correction. Indeed, these statements are imprecise. We are not limited to discrete spaces; in continuous spaces, the state space is infinite. We will correct this.\n\n> l.154-157: This claim needs stronger support to be that general. The experiment you show here is an illustrative example, too small to frame the takeaway so broadly.\n\nWe understand your concern regarding the strength of the statement about the extension of Q-values with subgoals. However, we believe that illustrative example prove the extension of Q-table works. Additionally, similar pattern has been used in the literature [1].\n\n[1] Ashley Edwards, Himanshu Sahni, Rosanne Liu, Jane Hung, Ankit Jain, Rui Wang, Adrien Ecoffet, Thomas Miconi, Charles Isbell, and Jason Yosinski. Estimating q (s, s’) with deep deterministic dynamics gradients. In International Conference on Machine Learning, pages 2825–2835. PMLR, 2020\n\n> l.160: Why are there fewer subgoal tuples? I understand that both methods create exactly one datapoint for every step. If that's because of duplicates in the buffer, then this example may not be fully relevant (as in other environments, it is nearly impossible to repeat exactly the same state).\n\nIn this experiment, we adopt the Q-learning algorithm. These tuples represent the cells in the Q-table.\n\nIn the example shown in Figure 3, $(\\mathcal{A} = \\mathcal{A}^o = \\{ \\text{none}, \\uparrow, \\downarrow, \\leftarrow, \\rightarrow \\})$ and $(\\mathcal{G} = \\{D_1, D_2\\})$. In the Q-table, the number of entries for $(s, g, a)$ is $(10 \\cdot |S|)$, which is fewer than the number of entries for $(s, a^o, a)$. \n\nDue to exploration, it is practically impossible to update all cells in the Q-table. During my experiments, I observed that the number of cells used in the Q-table with $(s, a^o, a)$ was indeed fewer.\n\n> l.297: I'd also mention here which value of H you've chosen.\n\nThe hyperparameters are presented in Appendix B.In both Foraging and Predator-Prey, the subgoal horizon $H$ is 5. In SMAC, $H$ is also 10.\n\nAppendix B lists the hyperparameters. The subgoal horizon $H$ is 5 for Foraging and Predator-Prey, and 10 for SMAC.\n\n> What is the speed of training and inference of OMG compared to Naive OM and standard RL baselines (wall time)?\n\nThe training and test times are shown in the table below. OMG requires additional training time to compute subgoals from the buffer, as described in Eq. 6 and Eq.7.\n\n|   | OMG | Naive OM | D3QN |\n|:-----:|:-----:|:-----:|:-----:|\n| training time (minutes) | 848 | 588 | 273 |\n| test time (minutes) | 38 | 36 | 28 |", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}]

Author rebuttal:
We have added two experiments in the PDF as follows:

* We have increased the number of seeds in the Predator-Prey model from 5 to 10 to reduce experimental error and enhance the reliability of our findings. 

* We have incorporated an ablation study on subgoal selection, where OMG-Random, OMG-1s, and OMG-3s represent subgoals selected from the opponent’s future states randomly, at the next step, and at three steps, respectively.

Meta-review: This multi-agent RL paper is on ad hoc teamwork and is built around the idea of inferring co-player subgoals. Reviewers mostly appreciated the paper's clear presentation, though one identified specific presentation issues which they said should be fixed in the final version. I also had a minor nitpick with the presentation too in that I noticed that the following reference, while deeply relevant to the paper, was missing from the discussion:

Vezhnevets, Alexander, et al. "Options as responses: Grounding behavioural hierarchies in multi-agent reinforcement learning." International Conference on Machine Learning. PMLR, 2020.

But presentation aside, no one raised very significant concerns with the novelty of the approach. Moreover, the model and its evaluation were seen as technically sound, and the reviewers appreciated the author's detailed responses during the rebuttal period.
Decision: Accept (poster)