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COURSE · AI2

Temporal AI: Time Series & Sequential Decision Making

AI טמפורלי: סדרות עתיות וקבלת החלטות רציפה

the probabilistic theory of time series forecasting and sequential decision making

Forecast, decide, and act under uncertainty over time

Year 313 weeks2h lecture + 2h practiceProject-based

About this course

Model data that unfolds over time and learn to make sequential decisions under uncertainty.

Course format. Thirteen weeks, four contact hours each: a two-hour lecture (concepts and theory) and a two-hour practice session. The course is project-based; teams carry one running project end to end and present it three times, in weeks 5, 8, and 13.
What you will build

Built an end-to-end forecasting and control agent in Python with PyTorch, statsmodels, and Gymnasium, coupling a neural sequence forecaster to a deep reinforcement-learning controller trained with DQN and PPO inside a simulated environment.

Expected outcomes

  • Formalize stochastic processes, stationarity, and autocorrelation for temporal data
  • Derive classical forecasting models including ARIMA and exponential smoothing
  • Build sequence models with RNNs, LSTMs, and temporal transformers
  • Define Markov decision processes with states, actions, rewards, and discounting
  • Derive the Bellman equations and prove value and policy iteration convergence
  • Implement value-based and policy-gradient reinforcement learning algorithms
  • Quantify uncertainty with predictive intervals and Bayesian decision theory
  • Evaluate forecasts and policies with proper scoring rules and backtesting
  • Apply exploration-exploitation strategies including epsilon-greedy and bandits
  • Deploy a sequential decision agent in a simulated environment

Key topics

  • Time-series forecasting
  • Sequence models
  • Reinforcement learning
  • Decision under uncertainty

Theoretical foundations

The concepts and results this course rests on.

  • stochastic processes, stationarity, and autocorrelation
  • ARIMA and exponential smoothing with maximum-likelihood estimation
  • recurrent networks and backpropagation through time
  • Markov decision processes and the Bellman optimality equations
  • temporal-difference learning and the policy-gradient theorem
  • multi-armed bandits, regret bounds, and Thompson sampling
  • Bayesian decision theory and expected-utility maximization

Prerequisites

This is a Year-3 course. It assumes the mandatory CS core: data structures and algorithms, operating systems, computer networks, databases, software engineering, and the core mathematics (linear algebra, probability and statistics, calculus, discrete mathematics). It additionally requires the specific prior courses listed below.

Course-specific prerequisites:

  • Machine Learning
  • Probability and statistics
  • Linear algebra

Weekly schedule 13 weeks · lecture + practice

Temporal foundations
Wk 1
Time series and stochastic processes
LectureWe define stochastic processes, stationarity, autocorrelation, and the decomposition of series into trend, seasonality, and noise.
PracticeLoad real time-series data, plot ACF and PACF, and test for stationarity.
ProjectFrame the running forecasting-and-control problem and load the target dataset.
Wk 2
Classical forecasting
LectureWe derive autoregressive, moving-average, ARIMA, and exponential smoothing models and the maximum-likelihood estimation behind them.
PracticeFit ARIMA and exponential smoothing baselines and backtest them.
ProjectEstablish classical forecasting baselines for the project series.
Wk 3
Probabilistic forecasting and uncertainty
LectureWe cover predictive distributions, prediction intervals, proper scoring rules, and calibration.
PracticeProduce probabilistic forecasts and score them with pinball and CRPS metrics.
ProjectAdd calibrated uncertainty bands to the baseline forecasts.
Sequence models
Wk 4
Recurrent neural networks
LectureWe derive RNNs, backpropagation through time, vanishing gradients, and the LSTM and GRU gating that fix them.
PracticeTrain an LSTM forecaster and compare against the classical baselines.
ProjectIntroduce a neural sequence forecaster to the project.
Wk 5
Temporal transformersPresentation
LectureWe adapt attention to sequences with causal masking and positional encoding for long-horizon forecasting.
PracticeTeam presentation: each team defends its problem specification, dataset, and metrics.
ProjectLock the specification and prototype a transformer-based forecaster.
Decision theory
Wk 6
Markov decision processes
LectureWe define MDPs, returns, discounting, value functions, and the Bellman optimality equations.
PracticeImplement a gridworld MDP and solve it with value iteration.
ProjectReframe the project as a sequential decision problem with an explicit MDP.
Wk 7
Dynamic programming and planning
LectureWe prove convergence of policy iteration and value iteration and discuss the contraction-mapping argument.
PracticeImplement policy iteration and compare convergence with value iteration.
ProjectCompute an optimal planning policy for the known-model version of the task.
Reinforcement learning
Wk 8
Model-free value methodsPresentation
LectureWe derive Monte Carlo and temporal-difference learning, Q-learning, and the exploration-exploitation dilemma.
PracticeTeam presentation: interim demo of a learned policy in the simulator.
ProjectTrain a tabular or function-approximated Q-learning agent.
Wk 9
Deep reinforcement learning
LectureWe cover DQN, experience replay, target networks, and the deadly triad of function approximation.
PracticeImplement a DQN agent and stabilize training with replay and target nets.
ProjectUpgrade the agent to deep value-based control on raw features.
Wk 10
Policy gradients
LectureWe derive the policy-gradient theorem, REINFORCE, advantage estimation, actor-critic, and PPO.
PracticeImplement an actor-critic or PPO agent and compare sample efficiency.
ProjectAdd a policy-gradient controller and benchmark it against the value agent.
Uncertainty and bandits
Wk 11
Bandits and exploration
LectureWe cover multi-armed bandits, regret bounds, UCB, and Thompson sampling.
PracticeImplement UCB and Thompson sampling and chart cumulative regret.
ProjectAdd principled exploration to the decision agent.
Integration
Wk 12
Forecast-driven decisions
LectureWe combine forecasting and decision-making through Bayesian decision theory and expected-utility maximization.
PracticeCouple the forecaster to the controller so predictions drive actions.
ProjectIntegrate forecasting and control into one end-to-end agent.
Capstone
Wk 13
Final defensePresentation
LectureWe synthesize probabilistic forecasting and sequential decision-making and survey open problems.
PracticeTeam presentation: final demo with backtests and an oral defense of design choices.
ProjectDeliver the integrated forecasting-and-control agent with evaluation results.
AI tools in this course.

Students use AI assistants to generate and refactor the statsmodels ARIMA baselines, the LSTM and temporal-transformer forecasters, and the Gymnasium environment and reward code, vibe-coding the DQN and PPO training loops. They prompt AI to synthesize simulated episodes and edge-case series, to wire reward shaping and replay buffers, and to set up Optuna sweeps. AI also helps read backtest plots and learning curves, explaining why a policy diverged or a forecast lost calibration.

Student project

Teams build one temporal decision agent that first forecasts a real time series and then acts on those forecasts inside a simulated environment. The project grows from classical baselines through neural sequence models into a reinforcement-learning controller, ending with an integrated forecast-driven decision policy.

Requirements

  • Build a working system, not a set of disconnected exercises.
  • Be original: a new system that solves a real problem, not a re-implementation of a tutorial or course demo.
  • Show real depth: real data, real users or realistic load, and engineering trade-offs that are measured rather than assumed.
  • Carry one running project from specification to a deployed, defensible result across the whole term.
  • Work in a team of three or four and defend the design at each of the three presentations (weeks 5, 8, and 13).

Example projects

Energy demand forecasting and storage controlInventory and supply-chain replenishmentAlgorithmic trading agentTraffic signal controlCloud autoscaling controllerRide-hailing fleet dispatchDynamic pricing agentSmart-grid load balancing

Assessment & grading

Grading is project-based, with no written exam. Teams of three or four present one running project three times.

ComponentWhat it coversWeight
Project · SpecificationPresentation 1 (week 5): problem, objectives, and architecture20%
Project · InterimPresentation 2 (week 8): the working system demonstrated live30%
Project · FinalPresentation 3 (week 13): end-to-end demo with oral defense50%

Tools & platforms

  • PyTorch: sequence model implementation
  • statsmodels: ARIMA and classical time-series models
  • sktime: unified time-series forecasting API
  • Prophet: decomposable trend and seasonality forecasting
  • Gymnasium: reinforcement-learning environments
  • Stable-Baselines3: reference RL algorithm implementations
  • Ray RLlib: scalable distributed RL
  • NumPy: numerical computation
  • pandas: time-series data handling
  • Matplotlib: forecast and policy visualization
  • Optuna: hyperparameter optimization
  • Weights and Biases: experiment tracking

Free online courses

Existing free, video-based courses this course can build on, for self-study or as a teaching basis.

In Hebrew · בעברית

Primary literature

Seminal works to read for graduate-level depth.

References

Books and resources link to an online or publisher page.

Role in each concentration

ConcentrationRole
Intelligent Software SystemsElective
Networking & Cyber SecurityElective
AI & RoboticsCore · Semester 1
AI and Quantum Computing for FinanceCore · Semester 1
Immersive Systems & Game DevelopmentElective
Defense Technologies & Autonomous SystemsCore · Semester 2