We propose Pgx, a suite of board game reinforcement learning (RL) environments written in JAX and optimized for GPU/TPU accelerators. By leveraging JAX's auto-vectorization and parallelization over accelerators, Pgx can efficiently scale to thousands of simultaneous simulations over accelerators. In our experiments on a DGX-A100 workstation, we discovered that Pgx can simulate RL environments 10-100x faster than existing implementations available in Python. Pgx includes RL environments commonly used as benchmarks in RL research, such as backgammon, chess, shogi, and Go. Additionally, Pgx offers miniature game sets and baseline models to facilitate rapid research cycles. We demonstrate the efficient training of the Gumbel AlphaZero algorithm with Pgx environments. Overall, Pgx provides high-performance environment simulators for researchers to accelerate their RL experiments. Pgx is available at https://github.com/sotetsuk/pgx.

Building systems that autonomously create temporal abstractions from data is a key challenge in scaling learning and planning in reinforcement learning. One popular approach for addressing this challenge is the options framework [29]. However, only recently in [1] was a policy gradient theorem derived for online learning of general purpose options in an end to end fashion. In this work, we extend previous work on this topic that only focuses on learning a two-level hierarchy including options and primitive actions to enable learning simultaneously at multiple resolutions in time. We achieve this by considering an arbitrarily deep hierarchy of options where high level temporally extended options are composed of lower level options with finer resolutions in time. We extend results from [1] and derive policy gradient theorems for a deep hierarchy of options. Our proposed hierarchical option-critic architecture is capable of learning internal policies, termination conditions, and hierarchical compositions over options without the need for any intrinsic rewards or subgoals. Our empirical results in both discrete and continuous environments demonstrate the efficiency of our framework.

We propose Pgx, a suite of board game reinforcement learning (RL) environments written in JAX and optimized for GPU/TPU accelerators. By leveraging JAX's auto-vectorization and parallelization over accelerators, Pgx can efficiently scale to thousands of simultaneous simulations over accelerators. In our experiments on a DGX-A100 workstation, we discovered that Pgx can simulate RL environments 10-100x faster than existing implementations available in Python. Pgx includes RL environments commonly used as benchmarks in RL research, such as backgammon, chess, shogi, and Go. Additionally, Pgx offers miniature game sets and baseline models to facilitate rapid research cycles. We demonstrate the efficient training of the Gumbel AlphaZero algorithm with Pgx environments. Overall, Pgx provides high-performance environment simulators for researchers to accelerate their RL experiments. Pgx is available at https://github.com/sotetsuk/pgx.

We present a Monte-Carlo simulation algorithm for real-time policy improvement of an adaptive controller. In the Monte-Carlo simulation, the long-term expected reward of each possible action is statistically measured, using the initial policy to make decisions in each step of the simulation. The action maximizing the measured expected reward is then taken, resulting in an improved policy. Our algorithm is easily parallelizable and has been implemented on the IBM SP1 and SP2 parallel-RISC supercomputers. We have obtained promising initial results in applying this algorithm to the domain of backgammon. Results are reported for a wide variety of initial policies, ranging from a random policy to TD-Gammon, an extremely strong multi-layer neural network. In each case, the Monte-Carlo algorithm gives a substantial reduction, by as much as a factor of 5 or more, in the error rate of the base players. The algorithm is also potentially useful in many other adaptive control applications in which it is possible to simulate the environment.

Case-based reasoning (CBR) is an experience-based approach to problem solving, where a repository of solved cases is adapted to solve new cases. Recent research shows that Large Language Models (LLMs) with Retrieval-Augmented Generation (RAG) can support the Retrieve and Reuse stages of the CBR pipeline by retrieving similar cases and using them as additional context to an LLM query. Most studies have focused on text-only applications, however, in many real-world problems the components of a case are multimodal. In this paper we present MCBR-RAG, a general RAG framework for multimodal CBR applications. The MCBR-RAG framework converts non-text case components into text-based representations, allowing it to: 1) learn application-specific latent representations that can be indexed for retrieval, and 2) enrich the query provided to the LLM by incorporating all case components for better context. We demonstrate MCBR-RAG's effectiveness through experiments conducted on a simplified Math-24 application and a more complex Backgammon application. Our empirical results show that MCBR-RAG improves generation quality compared to a baseline LLM with no contextual information provided.

We propose Pgx, a suite of board game reinforcement learning (RL) environments written in JAX and optimized for GPU/TPU accelerators. By leveraging JAX's auto-vectorization and parallelization over accelerators, Pgx can efficiently scale to thousands of simultaneous simulations over accelerators. In our experiments on a DGX-A100 workstation, we discovered that Pgx can simulate RL environments 10-100x faster than existing implementations available in Python. Pgx includes RL environments commonly used as benchmarks in RL research, such as backgammon, chess, shogi, and Go. Additionally, Pgx offers miniature game sets and baseline models to facilitate rapid research cycles. We demonstrate the efficient training of the Gumbel AlphaZero algorithm with Pgx environments. Overall, Pgx provides high-performance environment simulators for researchers to accelerate their RL experiments. Pgx is available at https://github.com/sotetsuk/pgx.

TIle networks were trained by a supervised learning procedure on a large set of sample positions evaluated by a human expert. In actual match play against humans and conventional computer programs, the networks demonstrate substantial ability to generalize on the basis of expert knowledge. Our study touches on some of the most important issues in net(cid:173) work learning theory, including the development of efficient coding schemes and training procedures, scaling, generalization, the use of real-valued inputs and out(cid:173) puts, and techniques for escaping from local minima. Practical applications in games and other domains are also discussed.

This paper examines whether temporal difference methods for training connectionist networks, such as Suttons's TO(') algorithm, can be suc(cid:173) cessfully applied to complex real-world problems. A number of important practical issues are identified and discussed from a general theoretical per(cid:173) spective. These practical issues are then examined in the context of a case study in which TO(') is applied to learning the game of backgammon from the outcome of self-play. This is apparently the first application of this algorithm to a complex nontrivial task. It is found that, with zero knowledge built in, the network is able to learn from scratch to play the entire game at a fairly strong intermediate level of performance, which is clearly better than conventional commercial programs, and which in fact surpasses comparable networks trained on a massive human expert data set.

We present a Monte-Carlo simulation algorithm for real-time policy improvement of an adaptive controller. In the Monte-Carlo sim(cid:173) ulation, the long-term expected reward of each possible action is statistically measured, using the initial policy to make decisions in each step of the simulation. The action maximizing the measured expected reward is then taken, resulting in an improved policy. Our algorithm is easily parallelizable and has been implemented on the IBM SP! and SP2 parallel-RISC supercomputers. We have obtained promising initial results in applying this algo(cid:173) rithm to the domain of backgammon.

Although TD-Gammon is one of the major successes in machine learn(cid:173) ing, it has not led to similar impressive breakthroughs in temporal dif(cid:173) ference learning for other applications or even other games. We were able to replicate some of the success of TD-Gammon, developing a competitive evaluation function on a 4000 parameter feed-forward neu(cid:173) ral network, without using back-propagation, reinforcement or temporal difference learning methods. Instead we apply simple hill-climbing in a relative fitness environment. These results and further analysis suggest that the surprising success of Tesauro's program had more to do with the co-evolutionary structure of the learning task and the dynamics of the backgammon game itself.