Jekyll2022-04-03T22:21:07+00:00https://royf.org/feed/publications.xmlRoy Fox | PublicationsRoy Foxroyf@uci.eduAnytime PSRO for Two-Player Zero-Sum Games2022-02-28T00:00:00+00:002022-02-28T00:00:00+00:00https://royf.org/pub/McAleer2022Anytime<p>Policy space response oracles (PSRO) is a multi-agent reinforcement learning algorithm that has achieved state-of-the-art performance in very large two-player zero-sum games. PSRO is based on the tabular double oracle (DO) method, an algorithm that is guaranteed to converge to a Nash equilibrium, but may increase exploitability from one iteration to the next. We propose anytime double oracle (ADO), a tabular double oracle algorithm for 2-player zero-sum games that is guaranteed to converge to a Nash equilibrium while decreasing exploitability from one iteration to the next. Unlike DO, in which the restricted distribution is based on the restricted game formed by each player’s strategy sets, ADO finds the restricted distribution for each player that minimizes its exploitability against any policy in the full, unrestricted game. We also propose a method of finding this restricted distribution via a no-regret algorithm updated against best responses, called RM-BR DO. Finally, we propose anytime PSRO (APSRO), a version of ADO that calculates best responses via reinforcement learning. In experiments on Leduc poker and random normal form games, we show that our methods achieve far lower exploitability than DO and PSRO and decrease exploitability monotonically.</p>Roy Foxroyf@uci.eduPolicy space response oracles (PSRO) is a multi-agent reinforcement learning algorithm that has achieved state-of-the-art performance in very large two-player zero-sum games. PSRO is based on the tabular double oracle (DO) method, an algorithm that is guaranteed to converge to a Nash equilibrium, but may increase exploitability from one iteration to the next. We propose anytime double oracle (ADO), a tabular double oracle algorithm for 2-player zero-sum games that is guaranteed to converge to a Nash equilibrium while decreasing exploitability from one iteration to the next. Unlike DO, in which the restricted distribution is based on the restricted game formed by each player’s strategy sets, ADO finds the restricted distribution for each player that minimizes its exploitability against any policy in the full, unrestricted game. We also propose a method of finding this restricted distribution via a no-regret algorithm updated against best responses, called RM-BR DO. Finally, we propose anytime PSRO (APSRO), a version of ADO that calculates best responses via reinforcement learning. In experiments on Leduc poker and random normal form games, we show that our methods achieve far lower exploitability than DO and PSRO and decrease exploitability monotonically.Temporal-Difference Value Estimation via Uncertainty-Guided Soft Updates2021-12-13T03:00:00+00:002021-12-13T03:00:00+00:00https://royf.org/pub/Liang2021Temporal<p>Temporal-Difference (TD) learning methods, such as Q-Learning, have proven effective at learning a policy to perform control tasks. One issue with methods like Q-Learning is that the value update introduces bias when predicting the TD target of a unfamiliar state. Estimation noise becomes a bias after the max operator in the policy improvement step, and carries over to value estimations of other states, causing Q-Learning to overestimate the Q value. Algorithms like Soft Q-Learning (SQL) introduce the notion of a soft-greedy policy, which reduces the estimation bias via soft updates in early stages of training. However, the inverse temperature β that controls the softness of an update is usually set by a hand-designed heuristic, which can be inaccurate at capturing the uncertainty in the target estimate. Under the belief that β is closely related to the (state dependent) model uncertainty, Entropy Regularized Q-Learning (EQL) further introduces a principled scheduling of β by maintaining a collection of the model parameters that characterizes model uncertainty. In this paper, we present Unbiased Soft Q-Learning (UQL), which extends the work of EQL from two action, finite state spaces to multi-action, infinite state space Markov Decision Processes. We also provide a principled numerical scheduling of β, extended from SQL and using model uncertainty, during the optimization process. We show the theoretical guarantees and the effectiveness of this update method in experiments on several discrete control environments.</p>Roy Foxroyf@uci.eduTemporal-Difference (TD) learning methods, such as Q-Learning, have proven effective at learning a policy to perform control tasks. One issue with methods like Q-Learning is that the value update introduces bias when predicting the TD target of a unfamiliar state. Estimation noise becomes a bias after the max operator in the policy improvement step, and carries over to value estimations of other states, causing Q-Learning to overestimate the Q value. Algorithms like Soft Q-Learning (SQL) introduce the notion of a soft-greedy policy, which reduces the estimation bias via soft updates in early stages of training. However, the inverse temperature β that controls the softness of an update is usually set by a hand-designed heuristic, which can be inaccurate at capturing the uncertainty in the target estimate. Under the belief that β is closely related to the (state dependent) model uncertainty, Entropy Regularized Q-Learning (EQL) further introduces a principled scheduling of β by maintaining a collection of the model parameters that characterizes model uncertainty. In this paper, we present Unbiased Soft Q-Learning (UQL), which extends the work of EQL from two action, finite state spaces to multi-action, infinite state space Markov Decision Processes. We also provide a principled numerical scheduling of β, extended from SQL and using model uncertainty, during the optimization process. We show the theoretical guarantees and the effectiveness of this update method in experiments on several discrete control environments.Count-Based Temperature Scheduling for Maximum Entropy Reinforcement Learning2021-12-13T02:00:00+00:002021-12-13T02:00:00+00:00https://royf.org/pub/Hu2021Count<p>Maximum Entropy Reinforcement Learning (MaxEnt RL) algorithms such as Soft Q-Learning (SQL) and Soft Actor-Critic trade off reward and policy entropy, which has the potential to improve training stability and robustness. Most MaxEnt RL methods, however, use a constant tradeoff coefficient (temperature), contrary to the intuition that the temperature should be high early in training to avoid overfitting to noisy value estimates and decrease later in training as we increasingly trust high value estimates to truly lead to good rewards. Moreover, our confidence in value estimates is state-dependent, increasing every time we use more evidence to update an estimate. In this paper, we present a simple state-based temperature scheduling approach, and instantiate it for SQL as Count-Based Soft Q-Learning (CBSQL). We evaluate our approach on a toy domain as well as in several Atari 2600 domains and show promising results.</p>Roy Foxroyf@uci.eduMaximum Entropy Reinforcement Learning (MaxEnt RL) algorithms such as Soft Q-Learning (SQL) and Soft Actor-Critic trade off reward and policy entropy, which has the potential to improve training stability and robustness. Most MaxEnt RL methods, however, use a constant tradeoff coefficient (temperature), contrary to the intuition that the temperature should be high early in training to avoid overfitting to noisy value estimates and decrease later in training as we increasingly trust high value estimates to truly lead to good rewards. Moreover, our confidence in value estimates is state-dependent, increasing every time we use more evidence to update an estimate. In this paper, we present a simple state-based temperature scheduling approach, and instantiate it for SQL as Count-Based Soft Q-Learning (CBSQL). We evaluate our approach on a toy domain as well as in several Atari 2600 domains and show promising results.Target Entropy Annealing for Discrete Soft Actor–Critic2021-12-13T01:00:00+00:002021-12-13T01:00:00+00:00https://royf.org/pub/Xu2021Target<p>Soft Actor-Critic (SAC) is considered the state-of-the-art algorithm in continuous action space settings. It uses the maximum entropy framework for efficiency and stability, and applies a heuristic temperature Lagrange term to tune the temperature α, which determines how “soft” the policy should be. It is counter-intuitive that empirical evidence shows SAC does not perform well in discrete domains. In this paper we investigate the possible explanations for this phenomenon and propose Target Entropy Scheduled SAC (TES-SAC), an annealing method for the target entropy parameter applied on SAC. Target entropy is a constant in the temperature Lagrange term and represents the target policy entropy in discrete SAC. We compare our method on Atari 2600 games with different constant target entropy SAC, and analyze on how our scheduling affects SAC.</p>Roy Foxroyf@uci.eduSoft Actor-Critic (SAC) is considered the state-of-the-art algorithm in continuous action space settings. It uses the maximum entropy framework for efficiency and stability, and applies a heuristic temperature Lagrange term to tune the temperature α, which determines how “soft” the policy should be. It is counter-intuitive that empirical evidence shows SAC does not perform well in discrete domains. In this paper we investigate the possible explanations for this phenomenon and propose Target Entropy Scheduled SAC (TES-SAC), an annealing method for the target entropy parameter applied on SAC. Target entropy is a constant in the temperature Lagrange term and represents the target policy entropy in discrete SAC. We compare our method on Atari 2600 games with different constant target entropy SAC, and analyze on how our scheduling affects SAC.XDO: A Double Oracle Algorithm for Extensive-Form Games2021-12-07T00:00:00+00:002021-12-07T00:00:00+00:00https://royf.org/pub/McAleer2021XDO<p>Policy Space Response Oracles (PSRO) is a reinforcement learning (RL) algorithm for two-player zero-sum games that has been empirically shown to find approximate Nash equilibria in large games. Although PSRO is guaranteed to converge to an approximate Nash equilibrium and can handle continuous actions, it may take an exponential number of iterations as the number of information states (infostates) grows. We propose Extensive-Form Double Oracle (XDO), an extensive-form double oracle algorithm for two-player zero-sum games that is guaranteed to converge to an approximate Nash equilibrium linearly in the number of infostates. Unlike PSRO, which mixes best responses at the root of the game, XDO mixes best responses at every infostate. We also introduce Neural XDO (NXDO), where the best response is learned through deep RL. In tabular experiments on Leduc poker, we find that XDO achieves an approximate Nash equilibrium in a number of iterations an order of magnitude smaller than PSRO. Experiments on a modified Leduc poker game and Oshi-Zumo show that tabular XDO achieves a lower exploitability than CFR with the same amount of computation. We also find that NXDO outperforms PSRO and NFSP on a sequential multidimensional continuous-action game. NXDO is the first deep RL method that can find an approximate Nash equilibrium in high-dimensional continuous-action sequential games. Experiment code is available at [https://github.com/indylab/nxdo].</p>Roy Foxroyf@uci.eduPolicy Space Response Oracles (PSRO) is a reinforcement learning (RL) algorithm for two-player zero-sum games that has been empirically shown to find approximate Nash equilibria in large games. Although PSRO is guaranteed to converge to an approximate Nash equilibrium and can handle continuous actions, it may take an exponential number of iterations as the number of information states (infostates) grows. We propose Extensive-Form Double Oracle (XDO), an extensive-form double oracle algorithm for two-player zero-sum games that is guaranteed to converge to an approximate Nash equilibrium linearly in the number of infostates. Unlike PSRO, which mixes best responses at the root of the game, XDO mixes best responses at every infostate. We also introduce Neural XDO (NXDO), where the best response is learned through deep RL. In tabular experiments on Leduc poker, we find that XDO achieves an approximate Nash equilibrium in a number of iterations an order of magnitude smaller than PSRO. Experiments on a modified Leduc poker game and Oshi-Zumo show that tabular XDO achieves a lower exploitability than CFR with the same amount of computation. We also find that NXDO outperforms PSRO and NFSP on a sequential multidimensional continuous-action game. NXDO is the first deep RL method that can find an approximate Nash equilibrium in high-dimensional continuous-action sequential games. Experiment code is available at [https://github.com/indylab/nxdo].Obtaining Approximately Admissible Heuristic Functions through Deep Reinforcement Learning and A* Search2021-08-04T00:00:00+00:002021-08-04T00:00:00+00:00https://royf.org/pub/Agostinelli2021Obtaining<p>Deep reinforcement learning has been shown to be able to train deep neural networks to implement effective heuristic functions that can be used with A* search to solve problems with large state spaces. However, these learned heuristic functions are not guaranteed to be admissible. We introduce approximately admissible conversion, an algorithm that can convert any inadmissible heuristic function into a heuristic function that is admissible in the vast majority of cases with no domain-specific heuristic information. We apply approximately admissible conversion to heuristic functions parameterized by deep neural networks and show that these heuristic functions can be used to find optimal solutions, or bounded suboptimal solutions, even when doing a batched version of A* search. We test our method on the 15-puzzle and 24-puzzle and obtain a heuristic function that is empirically admissible over 99.99% of the time and that finds optimal solutions for 100% of all test configurations. To the best of our knowledge, this is the first demonstration that approximately admissible heuristics can be obtained using deep neural networks in a domain independent fashion.</p>Roy Foxroyf@uci.eduDeep reinforcement learning has been shown to be able to train deep neural networks to implement effective heuristic functions that can be used with A* search to solve problems with large state spaces. However, these learned heuristic functions are not guaranteed to be admissible. We introduce approximately admissible conversion, an algorithm that can convert any inadmissible heuristic function into a heuristic function that is admissible in the vast majority of cases with no domain-specific heuristic information. We apply approximately admissible conversion to heuristic functions parameterized by deep neural networks and show that these heuristic functions can be used to find optimal solutions, or bounded suboptimal solutions, even when doing a batched version of A* search. We test our method on the 15-puzzle and 24-puzzle and obtain a heuristic function that is empirically admissible over 99.99% of the time and that finds optimal solutions for 100% of all test configurations. To the best of our knowledge, this is the first demonstration that approximately admissible heuristics can be obtained using deep neural networks in a domain independent fashion.Modular Framework for Visuomotor Language Grounding2021-06-20T00:00:00+00:002021-06-20T00:00:00+00:00https://royf.org/pub/Nottingham2021Modular<p>Natural language instruction following tasks serve as a valuable test-bed for grounded language and robotics research. However, data collection for these tasks is expensive and end-to-end approaches suffer from data inefficiency. We propose the structuring of language, acting, and visual tasks into separate modules that can be trained independently. Using a Language, Action, and Vision (LAV) framework removes the dependence of action and vision modules on instruction following datasets, making them more efficient to train. We also present a preliminary evaluation of LAV on the ALFRED task for visual and interactive instruction following.</p>Roy Foxroyf@uci.eduNatural language instruction following tasks serve as a valuable test-bed for grounded language and robotics research. However, data collection for these tasks is expensive and end-to-end approaches suffer from data inefficiency. We propose the structuring of language, acting, and visual tasks into separate modules that can be trained independently. Using a Language, Action, and Vision (LAV) framework removes the dependence of action and vision modules on instruction following datasets, making them more efficient to train. We also present a preliminary evaluation of LAV on the ALFRED task for visual and interactive instruction following.Improving Social Welfare while Preserving Autonomy via a Pareto Mediator2021-06-07T00:00:00+00:002021-06-07T00:00:00+00:00https://royf.org/pub/McAleer2021Improving<p>Machine learning algorithms often make decisions on behalf of agents with varied and sometimes conflicting interests. In domains where agents can choose to take their own action or delegate their action to a central mediator, an open question is how mediators should take actions on behalf of delegating agents. The main existing approach uses delegating agents to punish non-delegating agents in an attempt to get all agents to delegate, which tends to be costly for all. We introduce a Pareto Mediator which aims to improve outcomes for delegating agents without making any of them worse off. Our experiments in random normal form games, a restaurant recommendation game, and a reinforcement learning sequential social dilemma show that the Pareto Mediator greatly increases social welfare. Also, even when the Pareto Mediator is based on an incorrect model of agent utility, performance gracefully degrades to the pre-intervention level, due to the individual autonomy preserved by the voluntary mediator.</p>Roy Foxroyf@uci.eduMachine learning algorithms often make decisions on behalf of agents with varied and sometimes conflicting interests. In domains where agents can choose to take their own action or delegate their action to a central mediator, an open question is how mediators should take actions on behalf of delegating agents. The main existing approach uses delegating agents to punish non-delegating agents in an attempt to get all agents to delegate, which tends to be costly for all. We introduce a Pareto Mediator which aims to improve outcomes for delegating agents without making any of them worse off. Our experiments in random normal form games, a restaurant recommendation game, and a reinforcement learning sequential social dilemma show that the Pareto Mediator greatly increases social welfare. Also, even when the Pareto Mediator is based on an incorrect model of agent utility, performance gracefully degrades to the pre-intervention level, due to the individual autonomy preserved by the voluntary mediator.CFR-DO: A Double Oracle Algorithm for Extensive-Form Games2021-02-28T00:00:00+00:002021-02-28T00:00:00+00:00https://royf.org/pub/McAleer2021CFRDO<p>Policy Space Response Oracles (PSRO) is a deep reinforcement learning algorithm for two-player zero-sum games that has empirically found approximate Nash equilibria in large games. Although PSRO is guaranteed to converge to a Nash equilibrium, it may take an exponential number of iterations as the number of information states grows. We propose XDO, a new extensive-form double oracle algorithm that is guaranteed to converge to an approximate Nash equilibrium linearly in the number of infostates. Unlike PSRO, which mixes best responses at the root of the game, XDO mixes best responses at every infostate. We also introduce Neural XDO (NXDO), where the best response is learned through deep RL. In tabular experiments on Leduc poker, we find that XDO achieves an approximate Nash equilibrium in a number of iterations 1-2 orders of magnitude smaller than PSRO. In experiments on a modified Leduc poker game, we show that tabular XDO achieves over 11x lower exploitability than CFR and over 82x lower exploitability than PSRO and XFP in the same amount of time. We also show that NXDO beats PSRO and is competitive with NFSP on a large no-limit poker game.</p>Roy Foxroyf@uci.eduPolicy Space Response Oracles (PSRO) is a deep reinforcement learning algorithm for two-player zero-sum games that has empirically found approximate Nash equilibria in large games. Although PSRO is guaranteed to converge to a Nash equilibrium, it may take an exponential number of iterations as the number of information states grows. We propose XDO, a new extensive-form double oracle algorithm that is guaranteed to converge to an approximate Nash equilibrium linearly in the number of infostates. Unlike PSRO, which mixes best responses at the root of the game, XDO mixes best responses at every infostate. We also introduce Neural XDO (NXDO), where the best response is learned through deep RL. In tabular experiments on Leduc poker, we find that XDO achieves an approximate Nash equilibrium in a number of iterations 1-2 orders of magnitude smaller than PSRO. In experiments on a modified Leduc poker game, we show that tabular XDO achieves over 11x lower exploitability than CFR and over 82x lower exploitability than PSRO and XFP in the same amount of time. We also show that NXDO beats PSRO and is competitive with NFSP on a large no-limit poker game.A* Search Without Expansions: Learning Heuristic Functions with Deep Q-Networks2021-02-08T00:00:00+00:002021-02-08T00:00:00+00:00https://royf.org/pub/Agostinelli2021Astar<p>A* search is an informed search algorithm that uses a heuristic function to guide the order in which nodes are expanded. Since the computation required to expand a node and compute the heuristic values for all of its generated children grows linearly with the size of the action space, A* search can become impractical for problems with large action spaces. This computational burden becomes even more apparent when heuristic functions are learned by general, but computationally expensive, deep neural networks. To address this problem, we introduce DeepCubeAQ, a deep reinforcement learning and search algorithm that builds on the DeepCubeA algorithm and deep Q-networks. DeepCubeAQ learns a heuristic function that, with a single forward pass through a deep neural network, computes the sum of the transition cost and the heuristic value of all of the children of a node without explicitly generating any of the children, eliminating the need for node expansions. DeepCubeAQ then uses a novel variant of A* search, called AQ* search, that uses the deep Q-network to guide search. We use DeepCubeAQ to solve the Rubik’s cube when formulated with a large action space that includes 1872 meta-actions and show that this 157-fold increase in the size of the action space incurs less than a 4-fold increase in computation time when performing AQ* search and that AQ* search is orders of magnitude faster than A* search.</p>Roy Foxroyf@uci.eduA* search is an informed search algorithm that uses a heuristic function to guide the order in which nodes are expanded. Since the computation required to expand a node and compute the heuristic values for all of its generated children grows linearly with the size of the action space, A* search can become impractical for problems with large action spaces. This computational burden becomes even more apparent when heuristic functions are learned by general, but computationally expensive, deep neural networks. To address this problem, we introduce DeepCubeAQ, a deep reinforcement learning and search algorithm that builds on the DeepCubeA algorithm and deep Q-networks. DeepCubeAQ learns a heuristic function that, with a single forward pass through a deep neural network, computes the sum of the transition cost and the heuristic value of all of the children of a node without explicitly generating any of the children, eliminating the need for node expansions. DeepCubeAQ then uses a novel variant of A* search, called AQ* search, that uses the deep Q-network to guide search. We use DeepCubeAQ to solve the Rubik’s cube when formulated with a large action space that includes 1872 meta-actions and show that this 157-fold increase in the size of the action space incurs less than a 4-fold increase in computation time when performing AQ* search and that AQ* search is orders of magnitude faster than A* search.