Pommerman is a hybrid cooperative/adversarial multi-agent environment, with challenging characteristics in terms of partial observability, limited or no communication, sparse and delayed rewards, and restrictive computational time limits. This makes it a challenging environment for reinforcement learning (RL) approaches. In this paper, we focus on developing a curriculum for learning a robust and promising policy in a constrained computational budget of 100,000 games, starting from a fixed base policy (which is itself trained to imitate a noisy expert policy). All RL algorithms starting from the base policy use vanilla proximal-policy optimization (PPO) with the same reward function, and the only difference between their training is the mix and sequence of opponent policies. One expects that beginning training with simpler opponents and then gradually increasing the opponent difficulty will facilitate faster learning, leading to more robust policies compared against a baseline where all available opponent policies are introduced from the start. We test this hypothesis and show that within constrained computational budgets, it is in fact better to "learn in the school of hard knocks", i.e., against all available opponent policies nearly from the start. We also include ablation studies where we study the effect of modifying the base environment properties of ammo and bomb blast strength on the agent performance.

The word "deep" in "deep learning" refers to the number of layers through which the data is transformed. More precisely, deep learning systems have a substantial credit assignment path (CAP) depth. The CAP is the chain of transformations from input to output. CAPs describe potentially causal connections between input and output. For a feedforward neural network, the depth of the CAPs is that of the network and is the number of hidden layers plus one (as the output layer is also parameterized).

This paper investigates the motion planning of autonomous dynamical systems modeled by Markov decision processes (MDP) with unknown transition probabilities over continuous state and action spaces. Linear temporal logic (LTL) is used to specify high-level tasks over infinite horizon, which can be converted into a limit deterministic generalized B\"uchi automaton (LDGBA) with several accepting sets. The novelty is to design an embedded product MDP (EP-MDP) between the LDGBA and the MDP by incorporating a synchronous tracking-frontier function to record unvisited accepting sets of the automaton, and to facilitate the satisfaction of the accepting conditions. The proposed LDGBA-based reward shaping and discounting schemes for the model-free reinforcement learning (RL) only depend on the EP-MDP states and can overcome the issues of sparse rewards. Rigorous analysis shows that any RL method that optimizes the expected discounted return is guaranteed to find an optimal policy whose traces maximize the satisfaction probability. A modular deep deterministic policy gradient (DDPG) is then developed to generate such policies over continuous state and action spaces. The performance of our framework is evaluated via an array of OpenAI gym environments.

Real world applications such as economics and policy making often involve solving multi-agent games with two unique features: (1) The agents are inherently asymmetric and partitioned into leaders and followers; (2) The agents have different reward functions, thus the game is general-sum. The majority of existing results in this field focuses on either symmetric solution concepts (e.g. Nash equilibrium) or zero-sum games. It remains vastly open how to learn the Stackelberg equilibrium -- an asymmetric analog of the Nash equilibrium -- in general-sum games efficiently from samples. This paper initiates the theoretical study of sample-efficient learning of the Stackelberg equilibrium in two-player turn-based general-sum games. We identify a fundamental gap between the exact value of the Stackelberg equilibrium and its estimated version using finite samples, which can not be closed information-theoretically regardless of the algorithm. We then establish a positive result on sample-efficient learning of Stackelberg equilibrium with value optimal up to the gap identified above. We show that our sample complexity is tight with matching upper and lower bounds. Finally, we extend our learning results to the setting where the follower plays in a Markov Decision Process (MDP), and the setting where the leader and the follower act simultaneously.

The softmax policy gradient (PG) method, which performs gradient ascent under softmax policy parameterization, is arguably one of the de facto implementations of policy optimization in modern reinforcement learning. For $\gamma$-discounted infinite-horizon tabular Markov decision processes (MDPs), remarkable progress has recently been achieved towards establishing global convergence of softmax PG methods in finding a near-optimal policy. However, prior results fall short of delineating clear dependencies of convergence rates on salient parameters such as the cardinality of the state space $\mathcal{S}$ and the effective horizon $\frac{1}{1-\gamma}$, both of which could be excessively large. In this paper, we deliver a pessimistic message regarding the iteration complexity of softmax PG methods, despite assuming access to exact gradient computation. Specifically, we demonstrate that softmax PG methods can take exponential time -- in terms of $|\mathcal{S}|$ and $\frac{1}{1-\gamma}$ -- to converge, even in the presence of a benign policy initialization and an initial state distribution amenable to exploration. This is accomplished by characterizing the algorithmic dynamics over a carefully-constructed MDP containing only three actions. Our exponential lower bound hints at the necessity of carefully adjusting update rules or enforcing proper regularization in accelerating PG methods.

Learning effective representations in image-based environments is crucial for sample efficient Reinforcement Learning (RL). Unfortunately, in RL, representation learning is confounded with the exploratory experience of the agent -- learning a useful representation requires diverse data, while effective exploration is only possible with coherent representations. Furthermore, we would like to learn representations that not only generalize across tasks but also accelerate downstream exploration for efficient task-specific training. To address these challenges we propose Proto-RL, a self-supervised framework that ties representation learning with exploration through prototypical representations. These prototypes simultaneously serve as a summarization of the exploratory experience of an agent as well as a basis for representing observations. We pre-train these task-agnostic representations and prototypes on environments without downstream task information. This enables state-of-the-art downstream policy learning on a set of difficult continuous control tasks.

We consider the problem where $M$ agents interact with $M$ identical and independent environments with $S$ states and $A$ actions using reinforcement learning for $T$ rounds. The agents share their data with a central server to minimize their regret. We aim to find an algorithm that allows the agents to minimize the regret with infrequent communication rounds. We provide \NAM\ which runs at each agent and prove that the total cumulative regret of $M$ agents is upper bounded as $\Tilde{O}(DS\sqrt{MAT})$ for a Markov Decision Process with diameter $D$, number of states $S$, and number of actions $A$. The agents synchronize after their visitations to any state-action pair exceeds a certain threshold. Using this, we obtain a bound of $O\left(MSA\log(MT)\right)$ on the total number of communications rounds. Finally, we evaluate the algorithm against multiple environments and demonstrate that the proposed algorithm performs at par with an always communication version of the UCRL2 algorithm, while with significantly lower communication.

The overwhelming presence of categorical/sequential data in diverse domains emphasizes the importance of sequence mining. The challenging nature of sequences proves the need for continuing research to find a more accurate and faster approach providing a better understanding of their (dis)similarities. This paper proposes a new Model-based approach for clustering sequence data, namely nTreeClus. The proposed method deploys Tree-based Learners, k-mers, and autoregressive models for categorical time series, culminating with a novel numerical representation of the categorical sequences. Adopting this new representation, we cluster sequences, considering the inherent patterns in categorical time series. Accordingly, the model showed robustness to its parameter. Under different simulated scenarios, nTreeClus improved the baseline methods for various internal and external cluster validation metrics for up to 10.7% and 2.7%, respectively. The empirical evaluation using synthetic and real datasets, protein sequences, and categorical time series showed that nTreeClus is competitive or superior to most state-of-the-art algorithms.

In offline reinforcement learning (RL) an optimal policy is learnt solely from a priori collected observational data. However, in observational data, actions are often confounded by unobserved variables. Instrumental variables (IVs), in the context of RL, are the variables whose influence on the state variables are all mediated through the action. When a valid instrument is present, we can recover the confounded transition dynamics through observational data. We study a confounded Markov decision process where the transition dynamics admit an additive nonlinear functional form. Using IVs, we derive a conditional moment restriction (CMR) through which we can identify transition dynamics based on observational data. We propose a provably efficient IV-aided Value Iteration (IVVI) algorithm based on a primal-dual reformulation of CMR. To the best of our knowledge, this is the first provably efficient algorithm for instrument-aided offline RL.

Learning competitive behaviors in multi-agent settings such as racing requires long-term reasoning about potential adversarial interactions. This paper presents Deep Latent Competition (DLC), a novel reinforcement learning algorithm that learns competitive visual control policies through self-play in imagination. The DLC agent imagines multi-agent interaction sequences in the compact latent space of a learned world model that combines a joint transition function with opponent viewpoint prediction. Imagined self-play reduces costly sample generation in the real world, while the latent representation enables planning to scale gracefully with observation dimensionality. We demonstrate the effectiveness of our algorithm in learning competitive behaviors on a novel multi-agent racing benchmark that requires planning from image observations. Code and videos available at https://sites.google.com/view/deep-latent-competition.