Gellért Weisz

Gellért Weisz, András György, Tadashi Kozuno et al. · deepmind

We consider approximate dynamic programming in $γ$-discounted Markov decision processes and apply it to approximate planning with linear value-function approximation. Our first contribution is a new variant of Approximate Policy Iteration (API), called Confident Approximate Policy Iteration (CAPI), which computes a deterministic stationary policy with an optimal error bound scaling linearly with the product of the effective horizon $H$ and the worst-case approximation error $ε$ of the action-value functions of stationary policies. This improvement over API (whose error scales with $H^2$) comes at the price of an $H$-fold increase in memory cost. Unlike Scherrer and Lesner [2012], who recommended computing a non-stationary policy to achieve a similar improvement (with the same memory overhead), we are able to stick to stationary policies. This allows for our second contribution, the application of CAPI to planning with local access to a simulator and $d$-dimensional linear function approximation. As such, we design a planning algorithm that applies CAPI to obtain a sequence of policies with successively refined accuracies on a dynamically evolving set of states. The algorithm outputs an $\tilde O(\sqrt{d}Hε)$-optimal policy after issuing $\tilde O(dH^4/ε^2)$ queries to the simulator, simultaneously achieving the optimal accuracy bound and the best known query complexity bound, while earlier algorithms in the literature achieve only one of them. This query complexity is shown to be tight in all parameters except $H$. These improvements come at the expense of a mild (polynomial) increase in memory and computational costs of both the algorithm and its output policy.

Daniel Kane, Sihan Liu, Shachar Lovett et al. · deepmind

A fundamental question in reinforcement learning theory is: suppose the optimal value functions are linear in given features, can we learn them efficiently? This problem's counterpart in supervised learning, linear regression, can be solved both statistically and computationally efficiently. Therefore, it was quite surprising when a recent work \cite{kane2022computational} showed a computational-statistical gap for linear reinforcement learning: even though there are polynomial sample-complexity algorithms, unless NP = RP, there are no polynomial time algorithms for this setting. In this work, we build on their result to show a computational lower bound, which is exponential in feature dimension and horizon, for linear reinforcement learning under the Randomized Exponential Time Hypothesis. To prove this we build a round-based game where in each round the learner is searching for an unknown vector in a unit hypercube. The rewards in this game are chosen such that if the learner achieves large reward, then the learner's actions can be used to simulate solving a variant of 3-SAT, where (a) each variable shows up in a bounded number of clauses (b) if an instance has no solutions then it also has no solutions that satisfy more than (1-$ε$)-fraction of clauses. We use standard reductions to show this 3-SAT variant is approximately as hard as 3-SAT. Finally, we also show a lower bound optimized for horizon dependence that almost matches the best known upper bound of $\exp(\sqrt{H})$.

Gellért Weisz, András György, Csaba Szepesvári

We consider online reinforcement learning (RL) in episodic Markov decision processes (MDPs) under the linear $q^π$-realizability assumption, where it is assumed that the action-values of all policies can be expressed as linear functions of state-action features. This class is known to be more general than linear MDPs, where the transition kernel and the reward function are assumed to be linear functions of the feature vectors. As our first contribution, we show that the difference between the two classes is the presence of states in linearly $q^π$-realizable MDPs where for any policy, all the actions have approximately equal values, and skipping over these states by following an arbitrarily fixed policy in those states transforms the problem to a linear MDP. Based on this observation, we derive a novel (computationally inefficient) learning algorithm for linearly $q^π$-realizable MDPs that simultaneously learns what states should be skipped over and runs another learning algorithm on the linear MDP hidden in the problem. The method returns an $ε$-optimal policy after $\text{polylog}(H, d)/ε^2$ interactions with the MDP, where $H$ is the time horizon and $d$ is the dimension of the feature vectors, giving the first polynomial-sample-complexity online RL algorithm for this setting. The results are proved for the misspecified case, where the sample complexity is shown to degrade gracefully with the misspecification error.

Gheorghe Comanici, Eric Bieber, Mike Schaekermann et al. · amazon-science, baidu

In this report, we introduce the Gemini 2.X model family: Gemini 2.5 Pro and Gemini 2.5 Flash, as well as our earlier Gemini 2.0 Flash and Flash-Lite models. Gemini 2.5 Pro is our most capable model yet, achieving SoTA performance on frontier coding and reasoning benchmarks. In addition to its incredible coding and reasoning skills, Gemini 2.5 Pro is a thinking model that excels at multimodal understanding and it is now able to process up to 3 hours of video content. Its unique combination of long context, multimodal and reasoning capabilities can be combined to unlock new agentic workflows. Gemini 2.5 Flash provides excellent reasoning abilities at a fraction of the compute and latency requirements and Gemini 2.0 Flash and Flash-Lite provide high performance at low latency and cost. Taken together, the Gemini 2.X model generation spans the full Pareto frontier of model capability vs cost, allowing users to explore the boundaries of what is possible with complex agentic problem solving.

Qinghua Liu, Gellért Weisz, András György et al.

While policy optimization algorithms have played an important role in recent empirical success of Reinforcement Learning (RL), the existing theoretical understanding of policy optimization remains rather limited -- they are either restricted to tabular MDPs or suffer from highly suboptimal sample complexity, especial in online RL where exploration is necessary. This paper proposes a simple efficient policy optimization framework -- Optimistic NPG for online RL. Optimistic NPG can be viewed as a simple combination of the classic natural policy gradient (NPG) algorithm [Kakade, 2001] with optimistic policy evaluation subroutines to encourage exploration. For $d$-dimensional linear MDPs, Optimistic NPG is computationally efficient, and learns an $\varepsilon$-optimal policy within $\tilde{O}(d^2/\varepsilon^3)$ samples, which is the first computationally efficient algorithm whose sample complexity has the optimal dimension dependence $\tildeΘ(d^2)$. It also improves over state-of-the-art results of policy optimization algorithms [Zanette et al., 2021] by a factor of $d$. In the realm of general function approximation, which subsumes linear MDPs, Optimistic NPG, to our best knowledge, stands as the first policy optimization algorithm that achieves polynomial sample complexity for learning near-optimal policies.

Gellért Weisz, Csaba Szepesvári, András György

We consider the minimax query complexity of online planning with a generative model in fixed-horizon Markov decision processes (MDPs) with linear function approximation. Following recent works, we consider broad classes of problems where either (i) the optimal value function $v^\star$ or (ii) the optimal action-value function $q^\star$ lie in the linear span of some features; or (iii) both $v^\star$ and $q^\star$ lie in the linear span when restricted to the states reachable from the starting state. Recently, Weisz et al. (2021b) showed that under (ii) the minimax query complexity of any planning algorithm is at least exponential in the horizon $H$ or in the feature dimension $d$ when the size $A$ of the action set can be chosen to be exponential in $\min(d,H)$. On the other hand, for the setting (i), Weisz et al. (2021a) introduced TensorPlan, a planner whose query cost is polynomial in all relevant quantities when the number of actions is fixed. Among other things, these two works left open the question whether polynomial query complexity is possible when $A$ is subexponential in $\min(d,H)$. In this paper we answer this question in the negative: we show that an exponentially large lower bound holds when $A=Ω(\min(d^{1/4},H^{1/2}))$, under either (i), (ii) or (iii). In particular, this implies a perhaps surprising exponential separation of query complexity compared to the work of Du et al. (2021) who prove a polynomial upper bound when (iii) holds for all states. Furthermore, we show that the upper bound of TensorPlan can be extended to hold under (iii) and, for MDPs with deterministic transitions and stochastic rewards, also under (ii).

Gellért Weisz, Philip Amortila, Barnabás Janzer et al.

We consider local planning in fixed-horizon MDPs with a generative model under the assumption that the optimal value function lies close to the span of a feature map. The generative model provides a local access to the MDP: The planner can ask for random transitions from previously returned states and arbitrary actions, and features are only accessible for states that are encountered in this process. As opposed to previous work (e.g. Lattimore et al. (2020)) where linear realizability of all policies was assumed, we consider the significantly relaxed assumption of a single linearly realizable (deterministic) policy. A recent lower bound by Weisz et al. (2020) established that the related problem when the action-value function of the optimal policy is linearly realizable requires an exponential number of queries, either in $H$ (the horizon of the MDP) or $d$ (the dimension of the feature mapping). Their construction crucially relies on having an exponentially large action set. In contrast, in this work, we establish that poly$(H,d)$ planning is possible with state value function realizability whenever the action set has a constant size. In particular, we present the TensorPlan algorithm which uses poly$((dH/δ)^A)$ simulator queries to find a $δ$-optimal policy relative to any deterministic policy for which the value function is linearly realizable with some bounded parameter. This is the first algorithm to give a polynomial query complexity guarantee using only linear-realizability of a single competing value function. Whether the computation cost is similarly bounded remains an open question. We extend the upper bound to the near-realizable case and to the infinite-horizon discounted setup. We also present a lower bound in the infinite-horizon episodic setting: Planners that achieve constant suboptimality need exponentially many queries, either in $d$ or the number of actions.

Gellért Weisz, Philip Amortila, Csaba Szepesvári

We consider the problem of local planning in fixed-horizon and discounted Markov Decision Processes (MDPs) with linear function approximation and a generative model under the assumption that the optimal action-value function lies in the span of a feature map that is available to the planner. Previous work has left open the question of whether there exist sound planners that need only poly(H,d) queries regardless of the MDP, where H is the horizon and d is the dimensionality of the features. We answer this question in the negative: we show that any sound planner must query at least $\min(\exp(Ω(d)), Ω(2^H))$ samples in the fized-horizon setting and $\exp(Ω(d))$ samples in the discounted setting. We also show that for any $δ>0$, the least-squares value iteration algorithm with $O(H^5d^{H+1}/δ^2)$ queries can compute a $δ$-optimal policy in the fixed-horizon setting. We discuss implications and remaining open questions.

Gellért Weisz, András György, Csaba Szepesvári

We consider the problem of configuring general-purpose solvers to run efficiently on problem instances drawn from an unknown distribution. The goal of the configurator is to find a configuration that runs fast on average on most instances, and do so with the least amount of total work. It can run a chosen solver on a random instance until the solver finishes or a timeout is reached. We propose LeapsAndBounds, an algorithm that tests configurations on randomly selected problem instances for longer and longer time. We prove that the capped expected runtime of the configuration returned by LeapsAndBounds is close to the optimal expected runtime, while our algorithm's running time is near-optimal. Our results show that LeapsAndBounds is more efficient than the recent algorithm of Kleinberg et al. (2017), which, to our knowledge, is the only other algorithm configuration method with non-trivial theoretical guarantees. Experimental results on configuring a public SAT solver on a new benchmark dataset also stand witness to the superiority of our method.

Gellért Weisz, Paweł Budzianowski, Pei-Hao Su et al.

In spoken dialogue systems, we aim to deploy artificial intelligence to build automated dialogue agents that can converse with humans. A part of this effort is the policy optimisation task, which attempts to find a policy describing how to respond to humans, in the form of a function taking the current state of the dialogue and returning the response of the system. In this paper, we investigate deep reinforcement learning approaches to solve this problem. Particular attention is given to actor-critic methods, off-policy reinforcement learning with experience replay, and various methods aimed at reducing the bias and variance of estimators. When combined, these methods result in the previously proposed ACER algorithm that gave competitive results in gaming environments. These environments however are fully observable and have a relatively small action set so in this paper we examine the application of ACER to dialogue policy optimisation. We show that this method beats the current state-of-the-art in deep learning approaches for spoken dialogue systems. This not only leads to a more sample efficient algorithm that can train faster, but also allows us to apply the algorithm in more difficult environments than before. We thus experiment with learning in a very large action space, which has two orders of magnitude more actions than previously considered. We find that ACER trains significantly faster than the current state-of-the-art.